If I understand the original post correctly, you are talking about your friend acquiring a shotgun in Texas, and at some later date possibly exporting it to Canada.
The issue is not so much whether a specific shotgun can be legally owned in Canada. The problem will be in permanently exporting it from the U.S. The process is both time-consuming and expensive.
Major U.S. gunmakers can afford it since they get the paperwork done for a large shipment at a time, so cost per firearm is not too bad. For individuals exporting one or two firearms it becomes very expensive.
There are a few Canadian dealers who will arrange importation for individuals but the cost is around $250 per firearm, most of which is incurred by the U.S. exporter in getting approval. This doesn't include shipping costs.
For an individual in Canada, importing a firearm from the U.S. only makes sense if it is valuable, e.g. a custom made or collectible model, or if there's sentimental value.
If your friend moves to Canada he will need a PAL (possesion & acquisition license) to own a firearm in any case. Getting the license involves taking a firearm training/safety course, passing practical and written exams, plus a criminal background check.
Since he has to have the PAL anyway, it would be far simpler and cheaper just to buy a shotgun in Canada. As others have mentioned the key legal factors are overall length be at least 660mm, about 26 inches; and centerfire semiauto long guns are generally limited to five-round magazine capacity.
There's no minimum barrel length for rifles or shotguns provided overall length is at least 660mm and it is a factory original barrel. For example Cabelas in Canada sells Benelli pumps with 14" barrels. Other dealers show for sale an Italian-made Valtro pump with 13.5" barrel and detachable 7-round magazine, or a Norinco-made clone of the Remington 870 with 14" barrel (priced at the equivalent of $240 U.S., incidentally.)
Buying in the U.S. and then trying to export is really doing it the hard way.
