What is the ruling on communicating with a paternal aunt's daughter who is considered like a sister and friend, via social media, while she is in a distant country?

A female cousin is a non-mahram (definition) (a woman whom a man can marry), and it is not permissible to converse with her except under specific Islamic guidelines: that the communication is for a need and limited to that need, while avoiding temptation. This ruling is general, and considering her as a sister does not justify conversing with her unnecessarily.