first try some deoxit or another method to get the corrosion off the jack. if that no work...
get a small piece of double-sided foam tape and a bendable drinking straw.
put a small piece of the tape on the small side of the straw, on the outside where your mouth goes (tws...ehh)
stick it in the jack, then put a cord in to really squish the straw and tape onto the jack tip. pull out the cord carefully and check that the straw is secured to the jack. might take a few tries.
take off the nut and washer and gently feed it to the F hole, you'll find out if the wires are long enough. if not, you gotta crush the whole setup.
if so, do the same thing in reverse BUT don't use tape; tie the bottom end of the straw into a knot that is big enough to go in and out of the jack if you really tried. thread the straw through the jack, it should stop at the knot.
bend the drinking end of the straw to an "L" and feed the new jack back to the jack hole. When it is fed all the way through, put the nut on and then yank the straw out.