If I were to be asked, I'd rather tell H to leave out remarrying in his future plans since he has already been alone with the kids for some years. Choosing to be a good and supportive friend, here are some insights I am sharing with him and to those caught in the same dilemma.
Consider the kids - Ask whether the kids really need another parent. They are the ones who will find it difficult to adjust to the situation. Find a new partner whom they are going to like and accept like their real parent.
Consider your finances - Are you in debt at the moment? Be sure you have erased all your debts before remarrying. Remarrying can open you to another season expenses especially if you plan to have another kid.