Ah, the familliar chime of the annual FT tradition towards the end of the year asking what happens to nights around New Year. Very comforting indeed like putting on an old sweater.
Nights up to and including December 31 will credit to 2019 and nights from January 1 will credit to 2020 irrespective of checkin and checkout dates.
We will now hear various anecdotes of stays that have not posted like this and they may or may not be factually accurate based on our experience of Marriott IT. But do bear in mind that they are only anecdotes and the T&Cs are clear on this so if - for whatever reason - your stay over New Year does not post as described above then you should either keep quiet about it if it's in your favour or you can call Customer Support to fix it.