There was indeed cooperation between Hirtenberg and the East German ammunition factories. At least one of the DDR factories had Fritz Werner equipment, made in West Germany, that was shipped initially to Hirtenberg in Austria. There, I believe some test runs of ammo to be loaded on them were made. They were stripped of ID plates and passed on to the DDR.
After Reunification of the two Germanies, when authorities from the West inspected the factories, they were able to identify everything to do with the machinery because, as with most motor vehicle VIN plates, there were hidden ones usually known only to the factory. These were found upon inspection, perhaps with the assistance of the Werner firm.
This created quite a stir in Germany, and was even in the newspapers there. I think Fritze Werner Co. got some trouble out of it, warranted or not, and it probably created some “words” between the former West Germany (remember - unifiication) and Austrian authorities. Austrian was, and is, of course a neutral country in the post-WWII era, but in the beginning, at least, seemed to lean more towards the East than the West in some things. Their Army and I suppose some police agencies had a lot of Russian-Bloc small arms, which is why they manufactured the 7.62 x 25 mm Tokarev round, primarily to “feed” PPSh-41 SMGs in the Austrian service, I believe.
As to whether they made the 5.56 x 45 SS 109 ammo, I have no information to agree or disagree with that statement. I will say, though, that I believe that either of the two major ammunition manufacturers (04 and 05) in the DDR probably had the full capability to make any small arms cartridge of their choosing. The color tone of the bullet tip on the 04 88 and 04 89 5.56 x 45 rounds is the same metallic color as that used widely in the Soviet Bloc to identify tracer ammunition. It is somewhat different than the flat colors used by most of the west for tip markings, which is one reason why it was thought to be a tracer by many when they first appeared on the scene.
Just my thoughts. Again, I am not qualified to judge in which country those rounds were actually made.