What you have is a standard issue world war two German Mauser rifle. Many of these rifles were made, many were brought home, so there is a good likelihood that if your grandfather claims to have brought it back, he probably did. Without paperwork, its hard to prove, unless he took photos of it overseas or something. If you'd like to check a little further look over your gun for any markings stamped or engraved into it like "German" or "8mm," etc. These would be import marks, indicating that it was probably a commercial import for sale to consumers.
There are no issue records for these guns, so you will never know which soldier it was issued to or where. So, that avenue is closed.
Matching numbers:
When these guns were made, the parts had serial numbers stamped on them. Your gun is number "4111 v," and all of the parts would've had this serial number stamped on it. The bolt, however, is stamped 8874. This means that it came from another rifle and was placed into yours. As a result, it is "mismatched," which hurts the value somewhat. Feel free to post more pics and we can give more info.