Who is laying what can be a challenge. Even catching them in the act isn't conclusive for me. I've seen too many stay on a nest for a while and leave without laying an egg. Sometimes they move to another nest to lay, sometimes they just don't lay. Sometimes another hen gets in with her and lays an egg. How do you know there wasn't already an egg in the nest? In the act is a good clue but how badly do you want to know for sure?
I made some of my nests so I can lock a hen in and others out if I want to. When I catch a pullet or hen on the nest that I want to see what she is laying I lock her in and check that the nest is empty except for a fake egg. One of my goals is egg shell color. When I decide which to keep for my laying/breeding flock I really want to know what she is laying. It is quite important to me.
I have not tried this but some people have posted photos on here from when they tried it. I wish more would post photos. Early in the morning put some food coloring in her vent and look for colored streaks on the eggs. I've heard of people putting different colored lipstick on a hen's vent to do that but I'm not going to try to explain to my wife why I'm putting lipstick on a hen's vent. Especially if it is her lipstick.