If I understand this correctly, player A doesn't like player B, but player B has no issues with player A.
If that's correct, I'd say run the game, invite them both, and let player A decide if he's going to get over his issues or not.
Life's too short for drama.
The Wisdom of Solomon!

BTW my experience has been that the kind of person who says "I have issues with B" is inherently disruptive and in the longer term will either have issues with you too, or will behave in such an annoying way that you'll end up having issues with them. This may not apply if they're both good friends but my strong inclination would be to drop A and go with B.