Is the physical path to OneDrive TM folder exactly the same on both machines? Studio uses absolute paths for TMs and TBs, so if only a letter differs in the path, this error message will appear.

On a side note: storing anything on C is the worst idea I ever seen. Why not move the storage space to another drive?

Thank you

the only difference is the PC name 
C:\Users\*****\OneDrive - ******* Translations\Documents\SDL Trados Studio\Translation Memories

C:\Users\+++++\OneDrive - ******* Translations\Documents\SDL Trados Studio\Translation Memories

the [documents] is just a folder I called it and not the default documents folder of the PC. 

I can see different user names:

So the physical path is completely different. Locate OneDrive NOT in your users folder and the problem will be gone.

So the physical path is completely different. Locate OneDrive NOT in your users folder and the problem will be gone.

Thank you very much, I appreciate your help and efforts on this matter.
I have unlinked OneDrive on both machines and changed the folders on both machines out of C but still, I have two folders on 2 different computers. 
You cannot use the web-based files, do you? So, OneDrive creates a local folder no matter where it might be on each machine and now again Studio treats them as two different paths again and I get exactly the same error message 
I have created 10 test projects 5 on each machine and tried to open them from the other and the result was the same. 

If I got you wrong about your suggestion please correct me accordingly. 

Is the physical path the same on both machines?

This is what you see, when you go to OneDrive. But this cheats you about where the folder is. You need to see this:

This path must be identical.

Because I use a desktop and a laptop, I quite often have the situation, that I need to synchronize the PCs. However, I never put my files in the cloud. Instead, desktop and laptop have exactly the same paths for TMs and TBs. I use AllwaySync for synchronizing between desktop and laptop. This does not take much time and works much better than any cloud. I also copy the current project from desktop to laptop or the other way round.

Thank you

yes, apart from that on one machine it is D, and on the other it is E, I can make both D and try to see if that works! 
I will try this for the moment but still think there is something wrong with Studio defaults and they may address that as part of a cumulative update or service release (hopefully) later. 

Thank you Jerzy Czopik very much for all your help and support with this issue, I appreciate it as you did not leave me halfway and you directed me in the right direction.
for anybody else who may have a similar issue, now I have OneDrive on both PCs in a similar driver e.ge. drive F. so Studio may find the path easier. As I changed the Onedrive location twice and had many folders with the same name I restore Windows to a clean install again and now I have Studio working as before. Thank you to Jesús Prieto also for his input on this matter. 

Thank you for confirming it was a path issue.

I am glad it works now. Quite often a small reason cann cause big problems.