Ideally, the student would need to submit the assignment to you via the assignment submission. That way, you can use the SpeedGrader and some of the annotation tools (if you are wanting to use those) to grade the student's work. It may be marked as late (depending on any assignment settings you had set), but you might be able to work with the student to let him/her know it has been submitted on time. Here are a couple tutorials that might help:
Even if the student didn't submit the work to you like he/she should have, you should still be able to submit a grade for the assignment...it's just that the actual document that you were sent wouldn't be part of the assignment...as you cannot submit an assignment on behalf of a student.
I hope this will help a bit. Let Community members know if you have any other questions about this...thanks!