What files and folders should I copy to Linux so that everything I download now will be continue on the new system?
Tribler stores its data (private keys, reputation ledger, torrent state files) in its state directory. The state directory is created the first time you run Tribler. On Windows, it is located at C:\users\<username>\appdata\roaming\.Tribler. On Linux, the directory is /home/<username>/.Tribler. Some more information about Tribler state directory format can be found at this wiki page. Tribler stores downloaded files in its TriblerDownloads folder that is typically located in Windows Downloads folder.
However, Tribler torrent state files are platform-dependent, because they may include absolute file paths. So, the best way to move your installation to Linux is:
- Run Tribler once on Linux system, try downloading something, note the directory where the download goes and that
.Tribler directory is created correctly.
- Copy contents of
.Tribler directory from Windows to Linux overwriting everything but triblerd.conf.
- Copy contents of
TriblerDownloads folder into Linux TriblerDownloads folder.
- Edit each
.conf file in .Tribler/<version>/dlcheckpoints by removing engineresumedata and saveas lines. This can be done in a text editor or by using sed magic:
find ~/.Tribler -name "*.conf" -print0 |xargs -0 sed -i '/^engineresumedata/d'
find ~/.Tribler/7.5/dlcheckpoints -name "*.conf" -print0 |xargs -0 sed '/saveas = channels/!s/saveas = /d/'
- Run Tribler on Linux and wait for it re-checking all the downloads.
Please, report if it works for you. I’ll add it to our Wiki then 
Good luck 