OP, you're not being clear here.
Was your "backup" created with a backup application, such as time machine, CarbonCopyCloner, SuperDuper, or something else?
OR... is it just folders and files that you "copied yourself" to the external drive?
Take a screenshot of the folder/file hierarchy on the backup drive and post it here so we can see it.
If it's "just folders and files copied by hand", then you'll have to "re-construct" the drive "by hand". That means, copying things over a little at a time, until you have it pretty much as it was before.
That's what it sounds like you have.
If that's the case, you can't use Migration Assistant.
You're going to have to get a pencil and paper (to keep track of things).
Also, you need to do this (to overcome permissions problems):
a. connect the backup drive
b. let its icon mount on the desktop
c. click ONE time on the icon to select it
d. bring up the "get info" box (you can type command-i)
e. at the bottom of get info, click the lock and enter your password (the one you are using with the newly-installed Mojave)
f. put a checkmark into "ignore ownership on this volume" (in sharing and permissions)
g. close get info.
Now you can copy files from the backup and they will "come under the ownership" of your account on the Mojave OS.
If you don't do this, you could end up in "permissions hell".
Special info about copying things in the home folder.
You CANNOT COPY the "top level" of folders in your home folder into the new home folder.
That is... you can't copy the folders named "movies", "music", "pictures", "documents", etc.
HOWEVER -- you CAN copy files (and folders) that are INSIDE of these folders.
So you have to go through them one-at-a-time and move things carefully.
Good luck.
