I'm tasked with filling a website with content and the client has used the term "Falling to sleep". This doesn't sound right in my head to me, I would much rather use "Falling asleep". After doing some browsing of the web, I can't find any information on which one is better to use in a formal context.
It is in a bullet point list and the sentence is:
"Difficulty initiating (falling to sleep) or maintaining sleep (staying asleep)."