Hallo, based on plenty of experience upgrading RAM and HDs in various Fujitsu laptops I'd guess: Yes, NO problem! You never know? I never ever experienced a HD, SSHD (yes, cool!), SSD becoming refused. Just buy some good and large stuff. Actually it is standardized and that works fine. I personall have a 2 TB SSHD since many years in my A556G, cool!!
I regularly replace HDs by SSDs in old and very old Fujitsu A-series devices. Never ever experienced the slightest issue.
Completely independent you need to watch out for potenmtial issues MBR / UEFI and the like. No issue with Linux to migrate all data (do NOT clone as image from HD to SSD!) and get it booted.
I'd recommend: Just do it, nothing can go wrong (you can switch back - but you will not want to
)