NFA Transferrable Registered Sten Tube guns bring about $4000 to $5000 depending upon condition and build quality.
Keep in mind the the "Tube" designation basically means that the main receiver of the gun started out as automotive muffler pipe and had the cocking slot cut and a demilled Sten welded to it to create a Sten type machinegun. While these are mechanically identical to a real British Sten they are on the lower end of the machinegun totem pole from both a Sten collectible hierarchy as well as the overall transferrable machinegun market. (with only the "Mac" and Stemple Tube guns generating a lower average selling price)
The reference that it was inherited on an ATF Form 5 confirms that this gun most likely falls into the "transferrable" pool. (although there is technically an outside chance this is a Pre-86 dealer sample, meaning it was imported between 68 and 86 but your story doesn't lend itself to this outcome)
However, this particular example appears to be an uncut/never demilled genuine miltary capture and bringback it woudl certainly collect a higher premium in the collector market for folks who absolutely have to have an original gun vs. a clone or copy.
The analogy being that this Sten is the Original 1921A1 "Colt" Thompson vs a Auto Ordance "West Hurly, NY" gun. Mechanically and visually almost identical but one command a pricetag of $30K and the other $10K.
Not saying your Sten is work $30K but I would speculate that if you are patient and worth waiting for the right buyer to come along you would most certainly get a higher dollar than your average run of the mill Sten "Tube" gun.
Personally, I would contact the ATF NFA branch to confirm that they still have records of the registration (as their record keeping is sort of a well know mess) as you may have to send in a copy of the approved ATF F5 to get it back into the electronic system depending upon how long ago grandpa died. Better to get that confirmed/staightened out with the ATF prior to posting it for sale.
My suggestion to get more information would be to post your question on subguns.com as I specialize and collect post -WW2 machineguns and don't track WW2 bring back values much. Another alternate suggeston would be to contact Bob Naess at Black River Militaria as he would probably be able to give you a good frame of reference on valuation.
Then eventually put on ad on subguns, sturmgewehr for sale (as this is where the majority of online machinegun sales take place and you would get the most visibility).
Good luck with your sale and as others have mentioned I would try and do whatever I could not to let the gun out of your family.
James
Austin, Texas