my man's ex girlfriend keeps txtn him, he promises he wont answer but has in the past.

Ive had to threaten him If I found out he has responded to her calls/txts then we're done. He called me by her name last month and she just txted again to see how he's doing. He swears he isn't talking to her, but has lied in the past..what should i do he has asked me to marry him.