The answer depends what sort of access you have to the inside of the mast.
The simple solution is to attach a line (the line?) to another halyard and pull through, the problem is that you will get a certain amount of twist.
Alternative is to drop a weighted mousing line (see the other thread on renewing halyards - they all say don't use fishing line, I used kite string which I doubt is much different to mousing string) from one end and fish it out at the other.
Really drastic if you don't have any access to the inside - particulaly at the foot - will be to remove the end plate with sheeve and run the line up then thread the line through the sheeved endplate before re-attaching...
Might it be an idea to run a permanent mousing line up whilst your at it?
Of course it's possible ... unless your mast was built around the halyards!
Attach one end of a thin (mousing) line, longer than the mast, to a weight, for example a decent-sized shackle pin. Sew the other end of the line to the end of the halyard and lightly tape over the join so that it will run smoothly over the sheave. Take the weight to the top the mast (invite the previous owner to help with this bit!), feed it over the sheave and allow it to drop. Fish it out of the opening at the foot of the mast and then, gently, pull the halyard after it.