It is possible... but it will be expensive and there is no guarantee it will remove cleanly from the wood.
Depending on the location the other thing you have to consider is shipping the poster (and wood) to wherever it needs to be restored. This will of course significantly add to the bill and if the poster does not justify the cost then you will probably have to leave it.
In my case I was required to do the very same for an old Charlie Chaplin 1-sheet several years ago. It was sent to Poster Mountain who did an incredible job in 'lifting' it from an old wooden pallet and then linen back it. I sadly no longer have any pictures but the client (and I) were suitably gobsmacked by the results.
So depending on the poster I would suggest you send a picture and description to John at Poster Mountain to get an approximate quote and then factor in the additional shipping.
Good luck.