My ex keeps texting me

My ex & I of almost 2 years were in a toxic relationship. That's why I ended it with him & we broke up on a bad note. Not to mention, he found a new girlfriend less than week after breaking up that happened to be his coworker. 
I am now in a relationship with an amazing guy that treats me great. 
​BUT 
​Every couple of months my ex would text me checking up on me. And I know for a fact his girlfriend doesn't know. And I always ignore his texts. But recently I replied to his texts saying I'm happy with my new guy and he gets it. But i just want him out of my life for good. 
​So should I show his girlfriend the text messages and tell her to tell him to leave me alone? 

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