From Selection Info Palette >>Materials >> Category or Database, rigthclick in a free area and select Save Materials, then a menu will pop up, in that one Select the materials you want or all and save with a New name, then you will get a *.mat file that you can copy to a different version of TC and place in similar folder in different Version.
So back to Materials in palette in New version and rigthclick in free area and choose Database, it takes a little time for TC to load them all, then Load Materials and choose the *.mat file you just made and moved, ok and out.
If you dont have a preview thumbnail of them open that category and run preview on 1 of then, then Select that category and rigthclick and Select update Thumbnails for category, when finish, click add down in rigth corner and ok when it's finish.
A tip, start With 0 in the New mat file name, then it will come on top in category, aka 0 Jeffs.mat
V20, V21, 2015/ 16/ 17/ 18/ 19 Pro. Platinum
Deluxe 2015/ 16/ 19
Windows 10 Home Premium 64 bit, 32 GB
NVIDIA Geforce GTX 780m, 1 GB