Inheriting Time Machine Backup: Invalid Target
All relevant UUIDs and other Time Machine metadata are stored in /Library/Preferences/com.apple.TimeMachine.plist on the host side (the Mac to be backed up)! The file contains (probably the old) hostUUID (hardware), destination volume UUID (backup volume) and all IncludedVolumeUUIDs (source volumes). To get your current volume IDs use diskutil info diskXsY and the volumeID of the vanished Mojave volume is in the plist. The new hostUUID (hardware) and MAC are available in System Infomation.app > Hardware and Hardware > Ethernet-cards.

The com.apple.TimeMachine.plist may be populated with new UUIDs partly, you also have to grab the old com.apple.TimeMachine.plist from the backup.

All relevant Time Machine metadata on the side of the destination disk (the backup volume) are stored as extended attributes attached to the machine folder and subsequent snapshots and the included volumes:

machine folder

Example:

xattr -l /Volumes/Backup/Backups.backupdb/Haravikks\ Mac


and the volume folder(s) (in the latest backup of the old Mac). 

Example:

xattr -l /Volumes/Backup/Backups.backupdb/Haravikks\ Mac/2019-10-19-125832/Macintosh\ HD


(This is a lot of back &amp; forth. Best is to collect all data in some data sheet. Then it's easier to compare all plist entries/extended attributes and extract the proper ones)

After associating and inheriting a machine directory I expect various UUIDs and other data to be equal in the plist and the extended attributes on the one hand and the hardware/disk info of the new Mac on the other hand.

This is: BackupMachineAddress, HostUUID, ModelID and RecoveryPartitionVolumeUUID (
if available) on the host folder and various UUIDs in the plist.



If tmutil initiated inheritance fails, one has to use enforced adoption (or marry rich and get a larger backup drive):

To modify the extended attributs you have to read out (to reapply them later) and remove the ACLs of Backups.backupdb and Backups.backupdb/Haravikks\ Mac because both folders are heavily protected. Then apply new extended attributes (partly extracted from the plist and the new hardware info) and reinstate the ACLs you removed previously.

To get the ACLs use ls -le [folder1|2]. To remove the ACLs use sudo chmod -N [folder1] [folder2]. To apply new extended attributes use sudo xattr -w [ext_attr] [value] [/path/to/folder].

Examples:

If you found a ModelID Macmini4,1 in the extended attributes of /Volumes/Backup/Backups.backupdb/Haravikks\ Mac but the ModelID of the new Mac is Macmini8,1 you would have to update it like this:

sudo xattr -w com.apple.backupd.ModelID Macmini8,1 /Volumes/Backup/Backups.backupdb/Haravikks\ Mac


To update BackupMachineAddress (a MAC address of the new Mac) and HostUUID (the Hardware-UUID of the new Mac) use:

sudo xattr -w com.apple.backupd.BackupMachineAddress ac:87:b5:ca:c4:7a /Volumes/Backup/Backups.backupdb/Haravikks\ Mac
sudo xattr -w com.apple.backupd.HostUUID A7D80431-E567-389A-CC33-8321E461D431 /Volumes/Backup/Backups.backupdb/Haravikks\ Mac


To restore the ACLs use sudo chmod +a 'group:everyone deny ... writeextattr,chown' [folder1] [folder2]

Afterwards unmount the backup volume. Mount the backup volume again, open the Time Machine PrefPane and wait until the window is populated with the proper dest volume(s).



If you post all relevant data (which is a lot and somehow private) I could work out all commands properly.



This is untested and some "joy of experimentation" is required but it should work finally - somehow (|⚒)! At least it sheds some light on the files and attributes Time Machine uses to determine the validity of backup machine directories and what to change to re-establish assignments.