Is the submission of a document proving a husband's divorce from his first wife—for the purpose of registering his second marriage in Western countries, where laws do not permit marriage registration without the submission of such a document—considered a legitimate divorce, even if his intention was not divorce and the document was not issued by an official authority, given the necessity of registering the marriage to obtain legal residency?

First, seek another means besides writing down a divorce, unless you are compelled to do so and find no other way than to write it nominally, without the intention of enacting it or uttering it aloud. In that case, there is no harm in it. Divorce by writing does not take effect unless the writer intends it, and this is the view of the majority of jurists. However, if he writes it without intention, the preponderant opinion is that it does not take effect except with intention, and this is the saying of Abu Hanifa, Malik, and Al-Shafi'i; because writing may be for purposes other than enacting a divorce. And proceeding with writing without necessity is not advisable.