I would like to buy a good cover for TB20GT.
What do you think, is it possible to found somewhere an original cover?
I might be mistaken but I never heard of original covers (assuming you mean a cover manufactured / sold by Socata) for the TBs.
Is there a specific use you have in mind for a cover, e.g. a cover for the cockpit while travelling or a something a lot hardier to protect the whole plane while parked outside for extended periods?
There are a number of manufacturers on the market, e.g. Bruce’s custom covers in the US (https://www.aircraftcovers.com) or Jaxida covers in Germany (https://www.jaxida-cover.de). My travelling cover is from Jaxida, I have it for about 8 years now and are very happy with it. It is keeping very well and their service is exemplary. I recently installed an additional antenna on my plane, so I sent them my cover and they modified it with an additional antenna hat for EUR 80 incl. shipping within two days.
I use a Bruce’s Covers one too.
Not heard of Socata ever selling these but they may well have done so. They used to make heavy silver key rings, torches, and I even have a polo shirt. I wear t-shirts but posh (rich) people like pilots wear polo shirts But also the TB production ended c. 2001 so any original cover would now be pretty shagged. And would not fit any newly fitted antennae, etc.
Never heard of Jaxida; will check them out next time. Bruce’s have to be shipped from the US which adds to the cost. But they do really light and very effective lightweight reflective covers which is really the main reason. Sun does a lot of damage to the cockpit interior.