"Try The Gradual Approach"
This is definitely not coming just from her son. My guess is that she is giving out signals that yes, on some level, you are replacing her son's affections. Frankly, in my book that's a healthy new bond, but it's not healthy to make her son feel jealous, guilty, or displaced.
You Are Part Of The Family Too
So, what do you two do about it? I think that she has to make it really clear to herself, to you, and the son, that her new family includes you -- forever. She needs to create a special place for both of you so that the issues of jealousy, competition, and hostility are minimized.
I don't think you can eliminate these feelings, but ultimately enough trust should develop between you and her son that you both feel like you can deal with the feelings without letting them boil over into big "scenes."
Refrain From A Me Vs. Him Situation
So, go slow. I think the best strategy is to create a place where he feels safe and loved. Are there activities that the three of you can do together that he would really love? Are there ways that the three of you can come together as a family, yet make the son feel like he is still a very special person? Don't set it up as a dichotomy of me vs. him. It's really about how the three of you can come together as a whole.
His Father Might Be An Asset
I don't want to be too idealistic here. I think you are running into one of the hardest issues with divorce and the reformation of families. What role is the boy's father playing? He can be a safety valve if he is at all in the picture. What I mean is that there could be times when the boy's father could help out, not by removing him, but by encouraging him to accept you. But that is often impossible. To what extent can you and the boy relate individually?
If you can be friends with him, and make it clear that you can never really replace him in his mother's eyes, he could learn to trust you.