He may start the divorce process now. It doesn't matter who starts it. He also does not have to wait until his conditional green card expires. He will have to file an I-751 waiver. Here is some information on that:
Focus on where it says, "If your marriage was terminated other than by the death of your spouse, you must submit the following:"
He should submit evidence of the abuse to qualify under that category. That can be the police report, witness statements, etc.
He can and should also submit evidence similar to the evidence that he submitted at his marriage interview to show the marriage was real.
Here is a list of things that I like to give my clients and I know that he may not have all of these things, but the more he has, the better it is:
A letter where he describes, in a very detailed fashion, the circumstances in which he met his spouse, the reasons he married, and the feelings and emotions that he had or still has towards her, and why.
If they have a child or children together, the birth certificate for each child.
Wedding pictures and pictures of other moments when he and his spouse, and other members of each family and friends have been together.
Very detailed letters from people who know them and who are witnesses that their marriage was valid, who were at their wedding, or who knew them as a married couple.
Love letters or cards that they received from their spouse while in the relationship.
Letters from people addressed to both of them, or in which the person who wrote the letter refers to both them as a couple.
Any types of documents that have both their names on them that show that they bought a car, a house, furniture, or anything else together.
Any rental or lease agreements for their home or apartment with both of their names on it or a letter from the building manager or owner proving that they lived together.
Bank or financial statements that show that both had or have a savings or checking account together.
Any insurance documents that show that they were or still are covered by their insurance plan, or that his plan covers or covered her.
Bills, such as electricity, water, heat, cable TV, phone, or others that show both their names.
Jointly-filed Income tax papers (both their names).
An identification card that shows that his spouse's was using his last name.
Membership cards for video clubs, grocery stores or similar businesses, that show joint membership.
Any other documents.
While the focus will be more on the abuse than anything else, it is still good to at least show some proof that the marriage was real.
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