One of the nice things about working with mild steel is that it can be added to and subtracted from relatively easily! STENlings use a tube that was originally machined for use as a STEN, and converted to accept Sterling parts or appear to be a Sterling. To be converted to a Sterling, all of the holes along the length of the tube would have to be filled and recut to one extent or another!
The STEN cocking handle slot is to wide and wont retain the Sterling bolt handle, the STEN uses a trunion to retain the barrel at mid-length where the Sterling barrel is retained at the front. It would take twice as much work to convert a STEN to a Sterling but it could be done. I would expect that some conversions are being done that make it only appear to be a Sterling. This would be much easier, replacing the STEN endcap, adding the barrel shroud, stock and trigger assy. This conversion would not change the mag well and not allow the use of Sterling magazines.
As the value of Sterlings continue to rise I'm sure that someone will find it profitable to go to the added work required. The legality of the conversion is unknown to me.