Exactly what you mean "to know on server"?
Sure Mollify backend knows the user who has logged in, and server knows what is the current time (for the "when"), but you really don't describe where and how do you need this info? What do you want to achieve?
Certainly server does not know "what for" has user come, not until user actually does something (for which there are "events", which occur when user does something like delete a file). So you can write a plugin that listens for events, and then you know immediatelly (=when) when a user (=who) does something (=what, event tells what is the action).