[Mashiro]

Of course you have to connect both hard drives to the computer and in that case you have to mount both hard drives in seperate mount points (e.g. /mnt/hdd1 and /mnt/hdd2).

What do you mean with "use the hard drive again with the Linux operating system in addition to copying the hard drive information"? You should backup the data that you can backup to a seperate hard drive. I wouldn't use the broken hard drive afterwards.

It would be the best to backup all your data to something like a portable USB drive, remove the broken HDD, install the new HDD, install your OS and after that copy of the backed up files to your new OS on the new HDD/SSD.