You can get married and then file for his permanent residence (green card) on the basis of marriage to a US citizen.Â  After you get married and file, it should be about 4-6 months before you are called in for an interview with the local USCIS office and if everything is approved, he will receive the actual green card in the mail about 3-4 weeks thereafter.Â  If you are not looking to get married right away and he terminates his J1 visa, he will be out of status and it will be very difficult for him to legalize his status in any way since in order to change status, one must be in status.Â  The only option left to him if he falls out of status will be eventually to get married to a US citizen.