Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh

 

If they were married as Muslims, the marriage is still intact unless he has denounced Islam.

A person remains a Muslim as long as he has not denounced it.  The fact that he is slack in offering his prayers does not automatically take him out of the fold of Islam.

It is best that they both receive proper counseling.

Almighty Allah knows best.