Thousands of Syrians, Afghans and other refugees have made the perilous crossing of the narrow strait between the Turkish coast and islands such as Kos, Samos and Lesbos in recent weeks.
Mr Besmar was on one such dinghy during a pre-dawn crossing on August 27 when one of the 40 migrants on board accidentally dropped an oar into the water.
He volunteered to dive in and retrieve it but the sea was rough and he found himself dragged away by strong currents, unable to swim back to the dinghy. His fellow Syrian refugees just had time to throw him a life jacket before he disappeared in the darkness.
He drifted for hours and had given up hope of being rescued when he was spotted by Ms Tsiligeridu and her husband, Dimitri, a doctor, who at first thought the man in the water was a diver or snorkeler.
He slowed down the boat so as to avoid hitting the man but realised, as he approached closer, that the person was in extreme difficulties.
The Greek couple and their friends hauled the refugee out of the water. He was suffering from hypothermia and they wrapped him in towels and a jacket.
A photo of Ms Tsiligeridu cradling Mr Besmar was later posted on Facebook and has now attracted praise from as far afield as Australia and the US.
"He was nearly unconscious when we found him," Ms Tsiligeridu said on her Facebook page, where the photo has garnered thousands of comments, shares and 'likes'.
"He had sacrificed himself for his friends (by diving in to retrieve the oar)," the mother of three wrote. "We found him 13 hours later."
In an interview with La Repubblica newspaper, Ms Tsiligeridu, 42, denied that she was a heroine.
"I only did what any other human being would have done. Anyone else in my position would have done the same thing.
"He was trembling from hypothermia. He only managed to say, in English, 'My name is Mohammed Besmar and I come from Syria.' We wrapped towels around him to try to warm him up. We took him to Kos as quickly as we could.
"Before coming to the islands this summer I had no idea how bad the situation was. "The island is full of migrants, thousands of them are arriving every day. They sleep in tents in the street, they have no lavatories they can use, they are in a pitiful condition. Where are the European institutions in all this?
"When I was snorkelling with my daughter off Pserimos, we saw on the seabed some baby's clothes and Iraqi bank notes. And there was a damaged boat, right there on the beach. Women and children had probably landed there just a couple of hours before we arrived."
Mr Besmar was given medical help and now wants to reach Athens, from where he will continue his journey to western Europe.
In a Facebook message, he wrote: "I'm very sorry for having entered Greece illegally, but I had no other way of fleeing from the war that has destroyed my country. I was in the water for hours and I thought I was finished when the boat approached and Sandra saved me. I cannot find the words to thank her and the other people on board."
- The Telegraph
