Can facebook be used to prove cheating?

[Jasmine]

I have been married for almost 6 years. My husband is currently in El Salvador visiting his relatives for a month. We basically communicate via facebook since it's free to do because calling each other is really expensive. I have been getting messages from some female saying that she is with him. He denies it every single time and says that he has been faithful to me. She then sends me a picture of him holding her son in the water at the beach and says that they are happy as a family and that if I want her to stop bothering me, I need to stop contacting my husband. WTF?? Anyways, she has been logging onto his facebook and deleting me then blocking me. I had to create several facebook accounts and it's really making me mad. I've told him that if he did cheat that we will not be together and that he needs to come clean. He of course denies it. Now this female is not a looker by all means. She has been very disrespectful, calling me out of my name. She even logged onto his facebook and typed in English so I assumed it was him. She then typed in Spanish says that it was her and calling me out of my name being disrespectful. She obviously copied and pasted what he said in the last convo when he logged on. Should I give him the benefit of the doubt or leave his behind? I need concrete proof and it's his word against his. By the way, she has the audacity to call his mother "mother in law" in her facebook posts and he says that it's wishful thinking for her. What do I do?
* I meant to say it's his word against hers.
I will say that he has changed his password twice(so he says) but she keeps doing what she is doing. To me, I feel like something is going on. It's one thing to tell me the truth because then maybe, just maybe we can work through it. The fact that this girl is going on his page bothering me and disrespecting me and then he thinks that by ignoring it, the situation will go away, that is a red flag. I just need more concrete proof. I don't want to go to court looking foolish.
Oh and I do want to add that he did make another facebook page and everything seems fine at first. But then, she is at it again. I don't believe him when he says that nothing is going on. How can you create a new facebook page, change your password twice and still have this problem?
@Sophie.. it is until he returns in 2 weeks. Calling is very expensive and we thought it would be easier to just communicate via facebook. So that girl says that he is with her at the moment but then when I asked her to show me proof with her webcam that he is present, she says nothing. To me, either she is lying or he is lying.
@mmm... I agree. He says that he was at the beach with her family and his family and that they are friends. He also showed me pictures of him with his cousin's children but she just posted that on my personal facebook. I agree. She is bothering me because it's obvious that she wants him. He says that he doesn't want her and that I should pay no attention to her and that she is crazy. Originally, his son(now 16) had his facebook info and admitted that he gave it to the girl because he was mad.