You are a lucky guy! The M11 is one on my wish list and is an important part of US Military shotgun history.
Made from 1905 until 1947 or 49 depending on who's history you read, the M11 is a direct link to J M Browning (his patent) It was used in both World Wars. Your gun should be restored, maybe you can do it yourself, there are many general restoration videos on YouTube and advice on this site too. These are strong, relatively simple shotguns and should be preserved. Remington Heritage can probably date your gun and together with your Dads history of it, the gun should be passed down your family.
Below one of my favourite pics of an M11 in an unusual configuration (sorry for poor photo)
- M11USN.JPG (89.35 KiB) Viewed 3214 times