You need to install linux-oem-22.04c while still using your old intel motherboard (or wherever you can get your Pop OS installation to boot). After you’ve installed it you can transfer your storage to the new motherboard and you should be fine.
1- On your current Pop OS 22.04, run sudo apt install linux-oem-22.04c
You should see two files in /boot folder. initrd.img-6.1.0-1024-oem and vmlinuz-6.1.0-1024-oem
2- Create a folder in /boot/efi/EFI called OEM and copy these two files into that folder and rename them cp /boot/initrd.img-6.1.0-1024-oem /boot/efi/EFI/OEM/initrd.img cp /boot/vmlinuz-6.1.0-1024-oem /boot/efi/EFI/OEM/vmlinuz.efi
3- create an entry for systemd boot
cp Pop_OS-current.conf OEM.conf
4- Edit this file and change the title to something like OEM 6.1 and also change the lines starting with linux and initrd. All you need to do is to make sure those lines look like this linux /EFI/OEM/vmlinuz.efi and initrd /EFI/OEM/initrd.img
5- Edit /boot/efi/loader/loader.conf and add this line to the bottom timeout 5
Now you are ready to move your storage to the new motherboard.
6- On the new motherboard press F2 while booting and go into secure boot menu and disable secure boot.
7- When booting, systemd-boot will pop up in the start and you should see OEM 6.1 as one of the entries select that entry and press d on your keyboard to set that as the default.
You’ll probably need to reconnect to your wifi and re-roll your fingerprint, but everything should be working fine.
I have been unable to get Pop_OS working as of yet. Black screen issues during install and lots of hanging. I did end up getting it installed but no matter what I try I just get a black screen after logging in.