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You can associate your new internal drive with Time Machine, thereby allowing it to continue with backups. Of course, this means all of your backups from the past are gone. You can format the Time Machine drive after you restore, and then set it as the Time Machine destination as normal. (It's trying to prevent another disk with the same name from being backed up and causing problems with existing Time Machine backups.) However, Time Machine will not backup your new computer to that external drive because it recognizes that the identifier of the internal drive on your new computer doesn't match the identifier of the internal drive on your old computer. When you get a new Mac, you can use Migration Assistant, along with your Time Machine external drive, to restore your a backup to your new computer. Is it possible to re-establish Time Machine for a newer machine using the same disk as for the older machine (and the source of the migration image)? Now, I'll be doing the same thing soon, and my current Time Machine disk is barely a third (1/3) full, and I'd rather not purchase a new HD, and also rather not have to lose a few years worth of backups.
UPGRADE EXTERNAL HARD DRIVE TIME MACHINE PRO
Also, I was no longer able to access backups from before the migration, since the new MacBook Pro would not recognize the original Time Machine disk. This was a somewhat of a waste because the original Time Machine backup disk was less than half full.
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I'm not sure why, and as a result, I had to buy a new external HD for a new Time Machine backup. Everything copied correctly, however, when I tried to set up Time Machine on the new MacBook Pro using the original Time Machine disk, I was unable to. I used Migration Assistant and a Time Machine backup to load everything on to my then new(ish) MacBook Pro. I'm going to be migrating to a new machine in the new few weeks/months, and want to avoid something that happened during my last migration.