Here is a relevant article:
Trying to contact family in Puerto Rico? Here’s who to call (Miami Herald)
Excerpt:
As food and water have become more scarce, panicked family and friends
in the mainland U.S. and beyond are being advised by the territory’s
Federal Affairs Administration to do the following:
â–Ş Check the map below. Puerto Rico is divided into 12 zones. Each
zone is comprised of various municipalities. Phone numbers are listed
for all municipalities and for each region. These phone numbers will
connect you with the nearest Puerto Rico State Agency for Emergency
and Disaster Management office.
They can give you a better idea of what the conditions are like in
specific areas.

It’s likely that you won’t reach someone immediately, so be patient,
officials warn.
If you don’t know what municipality or zone your loved one is in, you
have a few options:
▪ Call the the Puerto Rico Federal Affairs Administration’s Washington
D.C. office at 202-800-3133 or 202-778-0710
Volunteers and staff are taking names and numbers and developing
databases to check the welfare of people who remain unreachable or
missing as the island begins to recover.
Officials say that agency is prioritizing emergency situations, like
people who are in [dire] need of medical attention. Staffers will reach
out to first responders on the ground and dispatch help. In the last
48 hours, the office has received more than 10,000 calls.
LINK TO MAP:
http://prfaa.pr.gov/wp-content/uploads/2017/09/Oficinas-Regionales.pdf
▪ Call the island’s government radio station WIPR at 787-777-0940 or
787-766-0505, which is helping people figure out what zones their
family members are in.
▪ Contact the island’s disaster relief team by e-mailing maria1@prfaa.pr.gov
Because of high volume, leaders are asking that you only send one
email — no follow-ups — unless the status of your loved one has
changed.
Include your contact information and as many details about your family
member or friend as possible.
â–Ş The American Red Cross is also helping via an online database,
where people can mark themselves safe.
To begin a search, contact your local Red Cross chapter. You can also
call our free national helpline at 844-782-9441 or use the
International Reconnecting Families Inquiry Form.
▪ Radio station WKAQ, which lost it’s roof during the storm,
continues to broadcast news and can be listened to online.
HOW TO HELP
â–Ş Email maria2@prfaa.pr.gov
â–Ş Call: 202-800-3134
Follow Monique O. Madan on Twitter: @MoniqueOMadan
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Really, it is much more likely that the survivors will reach out to loved ones as they are able.
Here you can see one way they are communicating back to the rest of the world:

And other ways:
Hurricane Maria victims in Puerto Rico struggle to connect with their families on U.S. mainland

The American Red Cross just put out a request for hams for Puerto Rico.
American Red Cross Asks ARRL’s Assistance with Puerto Rico Relief Effort (ARRL.org)
Excerpt:
09/24/2017
The American Red Cross (ARC) has asked the ARRL for assistance with
relief efforts in Puerto Rico. ARC needs up to 50 radio amateurs who
can help record, enter, and submit disaster-survivor information into
the ARC Safe and Well system. In the nearly 75-year relationship
between ARRL and ARC, this is the first time such a request for
assistance on this scale has been made. ARRL now is looking for radio
amateurs who can step up and volunteer to help our friends in Puerto
Rico.
The article continues on with the requirements for this service. It is all hands on deck there.
What every American needs to know about Puerto Rico’s hurricane disaster
Excerpt:
The storm knocked out 1,360 out of 1,600 cellphone towers on the
island. Many communities have been isolated from the outside world for
days, relying only on radios for news. National Guard members told the
Daily Beast they were struggling to communicate on the ground, making
their ability to respond to the disaster exceptionally hard. “There’s
no communication, that’s the problem,” said Capt. Jeff Rutkowski.

Puerto Ricans Are Hunting for Wi-Fi and Cell Signal to Contact Loved Ones (Time)
Excerpt:
(SAN JUAN, Puerto Rico) — Margarita Aponte and her relatives cleared
the road in front of her house with two oxen Sunday, then drove an
hour from her devastated hometown in central Puerto Rico to the old
telegraph building in the capital of San Juan.
There, thousands of Puerto Ricans gathered for a chance at a resource
nearly as precious as power and water in the wake of Hurricane Maria —
communication. "It's ringing, it's ringing, it's ringing!" Aponte, a
janitor, screamed as her phone connected to free Wi-Fi and her
Facetime call went through to the mainland.
Her eyes filled with tears as she talked with nephews, uncles,
brothers and sisters in Florida and Massachusetts for the first time
since Maria destroyed nearly every cellphone and fiber optic
connection on this U.S. territory of 3.4 million people.
The low murmur at one of two free Wi-Fi hotspots is occasionally
interrupted by the cheering of someone getting through the largely
jammed network. Most spend hours frowning at their phones, unable to
connect.
"There's no communication. We're in God's hands," Yesenia Gomez, a
kitchen worker, said as she left a message for her mother in the
neighboring Dominican Republic.
Dozens of other Puerto Ricans opted to pull over to the side of the
road along various highways where cellphone signals were strongest.
Carlos Ocasio, a maintenance worker, picked his way through tree
branches and broken glass bottles as he found a spot with a good
signal. Soon, he was able to reach his brother in New Jersey.
"My throat got a little choked up and I couldn't talk for a minute,"
he said. "They're calling me from everywhere, asking when I'm going to
arrive." Others in Puerto Rico and abroad called a local radio station
to provide names, numbers, exact addresses and pictures of their loved
ones in hopes of reconnecting.
But for hundreds of thousands of Puerto Ricans living on the U.S.
mainland, there has been only silence from the island.
Shirley Rodriguez, a resident of New York's Brooklyn borough, said she
has more than 30 relatives in Puerto Rico but she is especially
concerned about her 66-year-old mother, Mildred Rodriguez, who has
diabetes and pulmonary hypertension and lives in Hormigueros on the
island's west coast.
Rodriguez last spoke to her family before the storm and her relatives
were planning on being together for it. Since then, calls to their
cellphones have gone to voicemail.
"I'm absolutely numb at this point. It's a rollercoaster of emotion,"
she said. "Not knowing is extremely agonizing."
Her mother-in-law is in the San Juan area and somehow managed to
connect with someone who works for the mayor of Hormigueros, who was
able to tell Rodriguez that the area where her parents live escaped
flooding. But she still doesn't know what the actual conditions are
like.
Some in Puerto Rico expressed anger over what they said was a lack of
communication from cellphone providers about which towers were working
so they could drive in that direction.
"They're not giving us any information," said Ricardo Castellanos, a
business consultant. "We're in a state of emergency."