What do I do when my bf daughter says untrue things about him to me?

I have been in a relationship for 2 and half years. I have a strained relationship with his ex wife but a good one with his kids. His 20 year old daughter complains to me alot about how her father is cheap and doesn't help her mom. He pays 5,000 month child support/alimony towards the ex. He also pays her full college tuition(community college), books, car insurance, all car maintenance for his daughter. Whenever she needs extra spending money he always pays up(maybe to much, but thats not my bussiness).They have a good relationship (daughter and my bf) they talk everyday and see eachother on average 3 times a week. The ex wife told the daughter he is cheating them and doesn't help at all. It's really unfair to him. I truly like his daughter and she is still a little young to understand. It's very clear the ex is feeding her misinformation. I don't know if what if anything I should do when she gets really nasty - so far I have just kept quite and told my bf immediately after. He never sticks up for himself. He is done with his ex wife emotionally they had a poor marriage. Should he explain to his daughter how much he helps so she doesn't resent him? By the way me and his daughter are really close but lately the ex is trying to cause problems by slandering me I'm scared . I would appreciate real help and please read the rest of my questions if you want a full picture, thank you!