The man who divorced his wife is living in sin if he is living with another, and should never be given the idea that God is OK with it.
The Lord's will in this matter is clear:
" And unto the married I command, [yet] not I, but the Lord, Let not the wife depart from [her] husband:
11 but and if she depart, let her remain unmarried, or be reconciled to [her] husband: and let not the husband put away [his] wife." ( 1 Corinthians 7:10-11 ).
The same goes reciprocally...
The husband who departs should be reconciled to his wife, or remain unmarried.
That said, do not consider the new couple married, do not treat their relationship as legitimate in the eyes of God, and do not act as if it is.
Be gentle but be firm...
Your duty before the church is to reprove such things, and to emphasize the Lord's will in all matters.
Marriage is a sacred and holy covenant created by God;
We as believers in Jesus Christ should never treat it in any other fashion.