Electrical closet light add on from previous owner
I'm putting light in a closet. Conduit is run. Fixture is in ceiling for closet light. Wires are run from ceiling fixture {blue and white} to switch. Wire is run from switch for closet light to a three way switch in another room for power. There are three wires leading in to the three way switch two yellow and one brown. The wires from the closet switch are yellow and brown but not connected to the three way switch I ran the wires I bought yellow and brown since the wires leading to the three way are these colors.
My question is something does not seem right?
The wires run from the closet ceiling in the conduit were there from the previous owner. They are 14 ga. Blue and white. The wires for the switch to the three way are 14 ga. Brown and yellow which I bought. The previous owner had the conduit in place.
The three way has two yellow wires at the bottom and 1 brown wire on the top.
Can I connect the two wires I have run to the closet light switch and to the three way to get power make everything work and be in code. If so how would it be done?
The conduit has been there since I got there but I never knew where they connected. I fished to find the location for the other room.
I wanted to be sure because with the three way it adds an extra twist. I don't understand why they never ran the wires? I hope it is just because they never got around to it!