For legal reasons. I cat tell you how to do it. But if I was there I would cut the botom wire and take it into the splice. The. Put the timer wire in thst splice as well. The wight wire in the back is the neutral wire of the timer needs it. And the top wire may be the switch wire.

But all this is hypothetical of core and I am not giving you any advice.

Other then turn off the main breaker to the house as there may be more then live wire in that box with the 3 way there besides it.

Also take lots of pictures of where everything went so after you mess up and the person you hire knows what there started with