I live in Florida. My daughter is 15. Her biological father has never been in the picture since I was pregnant. I never pursued terminating his rights. I have been married now for over 10 years and she believes my husband to be her father calling him Dad since she was a baby. Just recently her biological father called me and asked if he could send her money for college. He says he has no intention of pursuing anything further but wanted to provide that to her. If I accept it and put it in to a trust account for her, am I establishing a relationship and opening the door for him to be a part of her life? I thought maybe I would accept it if he also send paperwork relinquishing his parental rights but am not sure if this legitimate...

Its not legitimate and accepting or denying money from him does not change anything. If he wished to pursue a relationship with her, he could do so through the court.

He cannot relinquish parental rights unless your husband wanted to adopt her. This is called a step parent adoption. It is a fairly simple process in FL if everyone is willing.

First the door is already open, and he has the right to go to court for visitation anytime he wants. So taking the money has nothing to do about it,

In fact you should have been getting child support all of these years, getting child support does not give any any additional rights he does not already have.

If your new husband wants to adopt, then you can get him to sign over his rights,

The paperwork will have to be court orders ( motions) to present to the court to be signed. You really need an attorney

There is a catch. He is in jail and may not ever be getting out...

There is a catch. He is in jail and may not ever be getting out...

Well, that makes it awfully hard for him to pursue using any of his rights. The only point of terminating his rights now would be for your husband to adopt.

As for the money... its free money and doesn't seem like it CAN come with a catch.