I already posted this here, but thought the game specific forum will be the first place people will search for a solution, like I was, hence the "double post".

For anyone who's wondering about whether existing saves can be used for Hitman Absolution:
I copied my save file hm5 from
C:\Program Files (x86)\Steam\userdata\STEAM-ID\205930\remote to
C:\Users\USER\AppData\Roaming\Io Interactive\HM5
and renamed it to save.dat as the GOG version calls it.

At first I thought the GOG version overwrote the save every time I launched the game, because nothing unlocked was displayed:
I had to finish the tutorial mission first so my completed save would suddenly take effect and all levels and unlocks became available.

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Edited a few minutes later: Fixed typo. Formatting(again).
Edit 2 two hours later: Fixed typo.