Spotted on r/freegames, follow the instructions in the picture in the link.
I had trouble getting this to work. My problem was that I had Episode One - Paris in my steam account. I had to go into the game in my steam library, select support and permanently remove this game from my account. Free for another 10 or so hours.
Step 0: Check if you have Hitman 1 DLCs in your steam account. If so remove.
Step 1: Open Hitman (2016) in the steam store and select Play Game but do not install
Step 2: Open Hitman 2 and install the starter pack (10gb).
Step 3: Start Hitman 2 and close. Either alt+F4 or quit through options.
Step 4: Right click Hitman 2 in your steam library and confirm the Legacy DLC is in your account. Steam should also start a 31.6gb update to Hitman 2.
HitmanTM1/2016/Season 1 has basically the same engine as HitmanTM2/2018/Season 2, so they have a "Legacy Pack" which puts the first game into the second as DLC. You will lose the original game launcher after this free weekend, but you will not lose the H2 DLC, in which the entire first game is playable in the second game's engine with upgraded features.