Question:How do you move on when your husband leaves you for another person, and he is a Christian who knows better?
I'm really sorry about your plight. It must be devastating.
The thing to keep in mind is that you can only do what is within your ability to control. Your husband was foolish to give up a wife and ultimately heaven for temporary pleasure. But knowing that won't put sense in his thick skull.
You didn't mention whether a divorce has occurred or not, but since he has broken the marriage covenant, it is your option to file for a divorce. That divorce does leave you the right to marry again if the opportunity arises (Matthew 19:9). If there is some hope that he will repent of his sin and seek reconciliation, and there is a willingness to accept him back, then I would urge you to wait a while before seeking another partner so that you might be able to reconcile (I Corinthians 7:10-11).
However, if that doesn't look likely, then take your time looking for a new spouse anyway. One mistake most people make is to jump for the first person who comes along because they want solace. Odds are, though, that the person will be worse than the one who left you, simply because the world is full of bad people. Another mistake that often happens is that you look for a man similar to your ex-husband because you are comfortable with that type of man. But you don't want a man just like your former husband; he had a character flaw that allowed him to leave his wife. There is no rush, be choosy about who you date and who you eventually decide to marry.
Another reason to deal finding another partner is if there are children involved. The stability of their lives have been ruined by their father leaving. While it is desirable to have a father in a child's life, adding another man adds complications that some children just can't handle. Consider moving close to your parents and have your father act as the stand in father as the children grow up. At least he will be familiar and provide stability in their lives.
If your former husband ever wakes up to his disastrous position and asks for your forgiveness, be prepared to forgive him and release him from his obligations to you. "For if you forgive men their trespasses, your heavenly Father will also forgive you. But if you do not forgive men their trespasses, neither will your Father forgive your trespasses" (Matthew 6:14-15). If there is already another man in your life, your forgiveness does not imply your willingness to remarry him. He was too late and lost that opportunity.
Your husband made his choice. You can't control that. You can choose, though, where you will go from here.