You're gonna transplant wild, (presumably thorny) blackberries into a fence row of barbed wire? Have you really thought about what you'll do at picking time? Seems like a "glutton for punishment" situation, lol. Another thing is pruning out the dead vines that have already born fruit. It will be easier if they're not on barbed wire. Just my opinion, but it's just as easy to pick the wild ones where they grow and plant thornless ones on a (smooth) fence.

I'm not so sure they are blackberries...I think they might be the invasive species of rose...the name escapes me right now...maybe somebody can chime in...
at any rate...I definately wouldn't want them on my fenceline, but if you really do, I guess there's no reason that you can't transplant them in the spring.

I would think that if you have an out of the way area, that you could do battle every year to keep them in check, would be your best bet, however getting the tame verities would be much less of a headache and there are some very good thorn less ones you could try...such as Chester triple Crown,
what ever your choice, remember, with the wild ones be prepared to do a major battle every year.

If the 'blackberries' are in the pic with the mailbox, then I agree with donnaz5. I don't think they're blackberries. either. The way new branches seem seem to come off the old canes looks like rose, not blackberry. I agree with her that they are probably Rosa multiflora, an invasive wild rose. Against a sturdy fence, they can be pretty, but they get big and heavy after just a few years, as they put out more and more canes.

I wouldn't bother to transplant any. The ones there will take over the fence before too long :]. You'll want to cut them back every few years, so they don't take the fence right down. Of course, as far as the cows are concerned, it would be a 'living barbed wire fence'.... So maybe that would be ok.