Restoring from File History created on old computer to a new computer

I'm thinking this should be easy, but it isn't turning out that way.

Computer A is dying, has a current File History. I am setting up Computer B and I want to use File History on B to restore from A. Instead, B can't see A's File History and just insists on creating its own. I don't want it to corrupt the backup on A's history

So the File History of A is on an external drive. I connect the external drive to B and go to File History. B just wants to write a File History of B and can't see the ones created by A.

Help, please!

Or am I just better off copying everything to an external drive and then copying it back to the new laptop?

OK, thanks for clarifying that. I'll carry on copying my stuff. :)

This has me rethinking the usefulness of File History. I thought that in the event of a catastrophe, such as hard drive failure, that File History provided some protection...as in, if you needed to replace your hard drive or your entire computer, all of your goodies would be safely backed up. However, if I can only restore to the original computer environment, where is the protection in that? If it were merely my hard drive being replaced, would I find myself unable to get at all of that File History? My hard drive actually is showing signs of failure, which is why I am migrating to a new computer and I thought I had things covered.

If this is the case, I am going to have to obtain some third party software, which I actually do have. I just haven't been using it because I was under the impression that the windows File History was just a smoother way of dealing with things.