I'm very much from the School of Nothing Ventured; Nothing Gained, so I'm with Debbie and Bass. I would cut off some nice cuttings to start, and then plant what's left of the crown too.
AND I would ask the neighbor if he wanted that stump out. If it's no more than 6-8 inches across (much bigger and it's not worth the work; and you can't get enough good roots with it) you should be able to get it out with a shovel, determination, and some good exercise.
I dig stumps this size up all the time with just a shovel. Start about 1.5 to 2 feet out from the center and dig a circle around the stump, keep circling and working your shove under further and further, trying to save as many roots as you can, and after some circling, digging under, and lifting, you should be able to pull the stump out, shake off the excess dirt, and move it to your place in a wheel barrow.
If the grounds not too hard, taking it out is not too hard either (but the opposite is also true). If you can do this, transplant it into some good dirt in a good spot, and I'll bet you roots will continue to grow starting this Fall, in the Spring you will get some strong new shoots, and you will have a nice fig bush and some figs next summer. The cuttings will work too but it would probably be two years plus before you get many figs.
Let us know how it goes.
Best wishes.
John
North Georgia Piedmont
Zone 7b