Advice needed about talking to my friends mom about him being transgender

So my friend is ftm and memorial weekend he came out to his mom in a letter. He is a guy of few words (and he also has terrible communication skills) so he didn't really explain anything to her, only saying "I believe I am a guy." And directing her to UppercaseCHASE1's channel. She texted him, "I love you." Right away but told him she was not going to change the name she uses for him because his father named him (they aren't together anymore.)
My friend is 15 years old and struggling with a lot of stuff, including depression and self-destructive behaviors. I told him that he has to talk to his mom about that stuff at least or I will do it for him. Or we could talk to her together. He's out of the state right now, but I told him the night he gets back we are talking to her. I have a feeling that I am going to end up being with him to talk to her or doing it myself. And I'm sure trans stuff will probably come up, especially if I use his chosen name when talking with his mom (I'll ask him what he wants me to do tho and respect that.)
I know quite a lot about trans stuff from youtube and tumblr, etc, as well as just listening to my friend. But it's still hard to explain it to people who don't really known anything about it. Any advice for me on how to have these discussions or resources I could pass on to her or him?
Thank you so much!