Chaos Strikes Back natively supports importing a Dungeon Master saved game from the same platform.
If you are in a mixed situation, like if you want to import a Dungeon Master for PC saved game into Chaos Strikes Back for Atari ST or Amiga, then it is not possible. The only workaround is to start a new game with regular Chaos Strikes Back champions from the Prison and then use DMute to modify the skills and statistics of these champions to match the ones of your Dungeon Master champions. However, a bug in DMute seems to prevent portrait import.
If you are using Chaos Strikes Back for Windows and Linux, you can play Dungeon Master with it, then copy the csbgame.dat file from the Dungeon Master folder to the Chaos Strikes Back folder and then use that saved game as a starting point to "Make a new adventure", just like if it was a saved game made in the Prison.
You can also load a saved game made with Dungeon Master for PC in CSBuild for PC v2.51, ignore the warning messages and then save the file. It will be converted to a format that can be loaded by Chaos Strikes Back for Windows.