Would you forgive him for texting his ex behind your back?

When I first started dating my boyfriend, he had told me he had been cheated on (he caught his ex in their bed w another dude) and was traumatized by it. He had this girl in his phone who kept texting him named Victoria, and one time she called when we were together and I had already tripped on him about it and was suspicious despite him saying she was just a friend he had known for 5 years, so he flipped his phone and said he did that to prevent me from 'causing problems'. I noticed one day his ex we will call her Britney, was still following him and he was following her on instagram and he refused to delete her saying they were not on bad terms and that he thought it would be mean etc, he said he wasn't even talking to her so there was no reason to delete her, I said but there is an open line of communication and he said no there is not. so he refused even though I told him it made me so uncomfortable and upset. Well, four months go by and come to find out Victoria was really Britney (he had her saved under her middle name which was Victoria) because he fell asleep and I went through his phone cus something felt wrong. I saw that he had even texted her "I love and miss you" on my fucking birthday and then later when I confronted him he apologized but kept insisting it was platonic and he did not want her. At one point i even confronted him and asked if Britney was really Victoria and he said no that's ridiculous, so he lied to my face and manipulated and gaslit me for fucking months. for the record I initially took him back then ended it because I realized how much better I deserve but he has been begging for me back so I wanted to know what you guys all think. He is also a bad boyfriend in other ways, during an argument where I said hey u should talk to ur psychiatrist u can't just get off lexapro without talking to a doctor, he said im making myself sound stupid, and then called me a crazy stupid bitch thinking I said it to insult him (I said it out of concern).

Would you forgive him for texting his ex behind your back?
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