I have a Samsung PM851 mSATA SSD that was installed on a motherboard which is now dead.
The drive has the hardware full disk encryption by Samsung, I used to put a password in Bios before the boot.
I have the password.
Windos cannot see the drive, however Samsun Magician does (the functions Encrypted Drive, PSID Revert and Secure Erase are not available for this drive.
How can I access the files from another machine?
Sounds like the encryption security is working as designed. It prevents someone from stealing the drive from its' parent machine and reading it on another computer. With the parent computer dead then the drive is a brick.
Unless you can revive the original motherboard the best you might be able to do (with the help of after market software) is erase it completely.
An Internet search of PM851 security should reveal a few links to possible solutions like AOMEI Partition software.