If they want you out of the country, it might be a good idea to pretend to them that you are leaving and let them find out in time (or not) that you haven't. Give them the address of some relative back home to send your mail to if they receive any. They will be happy thinking they won and you will be even happier. Moving from the address known to them to some other apartment or even another part of town might be a good idea.
If you feel that you must initiate the legal separation now in order to get your share, just be aware that if they put in a complaint against you and immigration starts to investigate, it looks bad for you. It doesn't matter if your marriage was not a marriage of convenience. It is a question of the marriage possibly having ended before you landed and if you should have reported that to them when you landed.