Time Machine and Switching Main Drive

I had two notebooks and swapped their HD's. My external Time Machine Backup does not recognize the old drive, in the new notebook as it's place to "backup". How do I force Time Machine to make the Backup on the external drive, without starting an entirely new backup?

 

Unfortunately, I have other computers backed up to the same external, so wiping it clean isn't really an option. The other reason is that the drive is nearly at capacity, and I rely on Time Machine just to delete the oldest backup to write new data.