I am a student on a short term Schengen visa in Belgium. Recently, my passport was stolen after which I got a new passport issued by the Indian embassy. This obviously does not have a Schengen visa (that was on the stolen passport). I have copies of all the stolen documents and the police report. With these, is it okay to travel within the Schengen countries? The visa expiry is still another month away, though I don't know if it is now rendered invalid for travel. Any suggestions?
My understanding is that, since you have entered Schengen legally with a valid visa, you may continue to stay in Schengen; and because there are no border controls within Schengen, you may also continue to travel within Schengen. You will definitely want to carry your passport, visa and police report copies though, just in case you're stopped by police etc. And you'll probably want to double-check this advice with eg. the embassy of the country you plan to visit, since I'm having a hard time finding a definitive source for this.
You'll definitely be able to leave Schengen normally, since your visa details for the old passport will be on file, although you should allow some extra time at the airport for checking. However, after you leave, you will not be able to come back unless you get your visa reissued, and you will apparently be charged the full new visa fee for this. Since you only have a month left and apparently have no plans to travel outside Schengen, this is most likely not worth it.