[Lulu]

I have a plot which is miles away from my home and is the only functioning full plot on site.  the rest of the site has been left to wild and the blackberries are taking over.  I have on this plot about 20 raspberry canes - can they be moved to new plot and if so - how and when ??  The  Joan Jay are rather lovely and I would
I've to keep them

[Ivor Backache]

Joan J is an autumn fruiting plant. Mine are flowering/setting at the moment. After fruiting the tops will die back and will be removed. Fresh growth will appear next year.
In your situation I would let them finish growing, cut them back (say October)  and then they can be dug up and replanted.