Basically, as I see it, you have the following options:
1) Assume that the relationship that "B" has with his 'significant other' is strong enough for her to see through "A"'s lies, or
2) Move away so that "A" has a hard time talking to "B"'s significant other, or
3) Have "B" cut the phone lines at "A"'s house and residence so that "A" cannot call "B"'s significant other, or
4) Have "B" slash the tires of "A"'s car so that "A" cannot travel to "B"'s and talk with "B"'s significant other, or
5) Have "B" break "A"'a legs so that he can't walk or crawl to "B"'s and talk with "B"'s significant other, or
6) Have "B" beat the hell out of "A" and say, "There is more where that came from!", or
7) Any combination of the above.
Please let me know if I have missed any....