Thank You all for the infos: as a matter of fact here in Italy it seems to be a bit easier to find a 3HW (or part of it).
After WWII all the militar relics left by Allied & German/Italians were sent to special areas called "ARAR" (Aree Raccolta Alienazione Residuati) that more or less means "concentration and alienation surplus area".
In those places vehicles that couldn't be used any more because too damaged were disassembled in order to recover metal or, in case they could be used again, sold to people who needed them.
Thanks to this some italians could start a transportation businness using for example GMC trucks and those who needed a motorbike could buy there one.
This businness lasted up to the beginning of '50s: my Triumph comes from one of this ARAR camps (may be in the area from Asti-Alessandria) and I was told that the cost of a motorcycle (complete but not working) was about 4 month of a worker salary.
Even if in the abyss in which Italy felt in those years, this was a businness opportunity too: many workshop started their activities thanks to "civilization" of military motorcycles.
They used to paint them in black color, chrome the tank and, this is interesting, modify the rear rigid frame assembling a suspension in order to improve the confort.
Benelli restarted its activity after war selling these suspension in kit adapted to the different models.
Due to good engine performance, Triumph 3HWs were preferred for race (motocross too); engine was tuned and front suspension was taken from telescopic Matchless.
Here is my 3HW: it was built in April '43 (under seat is written "TEC443"), frame is marked TL37887 and engine 3HW47887. It took me 3 years to rebuilt it (it was just a mess of pieces...) but now it runs fine.