Wire puller
I've used a puller for electrical wire--available from the local hardware store. It's a piece of springy flat wire with a hook on the end. You insert it where the line comes out of the boom and "fish" for the end of your line. Pull it gently back out.If you're unable to fish the line out, remove the cap at the end of the boom, pull the line out and attach it to the end of the wire, then push both back through the boom. The rigidity of the wire puller should enable you to move the line through the boom and back over the pully at the mast end. If not, you can use the other end of the wire puller to hook them and pull out.