Just to confirm the precise situation that's involved here...
Are you indicating that if you boot the system from the newly-cloned "new" HDD while that HDD is connected to the laptop as a USB external device, the system will boot to the OS (Desktop) of the newly-cloned "new" HDD? Is that what you're indicating?
Is that what you mean when you say the newly-cloned "new" HDD is "plugged in via USB adapter and can boot to it via changing BIOS."?
And if so, while the newly-cloned "new" HDD is still connected to the laptop as a USB external device and you remove or disconnect the internally-connected "old" HDD, are you indicating that you can boot to the OS (Desktop) booting from that USB externally-connected "new" HDD?
But when you internally install that newly-cloned "new" HDD in the laptop the system will not boot to the OS.
All the above comments/questions are just a suspicion on my part that's what's really involved here is a disk-cloning operation that has gone awry for one reason or another. So that the "new" HDD is NOT a bootable device. That when the system booted to the OS (Desktop) while the newly-cloned HDD was still connected as an external USB device, the system, was still booting to the internally-connected HDD and not to the cloned USB-connected HDD.
Naturally I may have misunderstood your query and may be wrong with my "diagnosis". So pardon me if I am.