Upvote:2
The steps are as follows:
Now, as you are in the US - your I-94 and I-20 prove your legitimate entry; and on exit there are no immigration formalities - so you are safe there.
On return you'll have to re-apply for your visas and explain that your passport was reported lost (this is where the police report comes in handy). You may then have to provide additional documents and be granted a new stamp on your passport.
The validity will probably remain the same as your old visa - so make sure your current passport meets the requirements for the visas you are trying to re-apply for.
In other words, if your old passport was valid till 2020 and you new one is temporary and only valid till March 2018; if a visa was valid till May 2018 it probably won't get stamped onto your replacement passport.
Upvote:8
They don't dig up your visa history, nor can they issue foreign visas.
Next time you travel abroad, you will have to apply for a new visa at the US embassy/consulate before going back, providing your I-20 and explaining that you lost your old passport.