I need help!! I would like to know what year my Papa Bear Chair is from?  

I'm going to go with A.P. Stolen inspector number.
Here are four differnet photos of Papa Bear undersides, showing different number marks, including your #7.
I believe the model number for this chair was AP-19

That makes perfect sense, is there anyway to figure out the exact year the chair was made?  I would never part with it just curious in its history.

I don't believe there is any direct way to know. 
You would have to find some indirect way of knowing. AP Stolen went out of business fairly early, so that puts a hard end date on the window.  If it was purchased in the USA, for instance, that probably eliminates nearly the whole first decade, just because Danish Modern wasn't a big thing for about that much time.

leif,
Do all Papa Bears have horsehair stuffing or did they switch to another material at some point?

Don't know. But I would be suspicious without horsehair. (Note that it isn't horsehair everywhere. The rear is different fiber).The chair is vey old fashioned inside, so a departure from that would be suspicious to me. 

Oh, and please make sure you are getting the chair done by somebody good. There are way to many butcher jobs done on this poor chair.
It shouldn't look or be overstuffed. The welt should leave the paw in a straight line. It needs to have the darts sewed into the back to have the right shape. It is hand stitched (except the darts in the back), and can't be done right without this hand stitching.
The cushion is the hardest of all.  It is supposed to have a pair of custom molded -latex- foam innards. And latex foam has a much more rubbery feel than the much cheaper polyurethane foam. And the only seam is at the welt around the perimeter. No folds at the corners, no seams at the corners. And for the love of god, don't overstuff it. 

Thanks for the info Leif, I will update with photos. The wood working is done, there was a split in the wood and it also required some refinishing on the arms and legs, and is now in the hands of the upholsterer.  I have decided to stay with the original colour.

For what it's worth, rubberized hair padding is still available from upholstery supply places.  It's been in continuous use for many decades.  

Thank you Spanky!  I didn't know the name of that stuff, so I couldn't find it.  I just reused the old stuff when I re-did my Papa Bear. 
The very center of the Papa bear seat is made of two layers of that stuff.  To make the cushion, you spray adhesive the fabric directly to the shaped latex foam cushion half, put a layer or rubberized horsehair on top, and hand stitch the fabric to the rubberized horsehair. Do the same for the other half. Then you hand stitch the welt onto the edge of one of these halves, and finally stitch both halves together. 
The fact that there is nothing between the latex foam and the fabric makes it very challenging to make the cushion, because the surface of the foam needs to be very smooth.  And without a custom molded piece of foam, you have to carve the foam by hand to the right shape and smooth. And the you have to slightly stretch the fabric and hand stitch it onto the rubberized hair pad, which is tricky, because there is nothing solid to stretch against. 
That cushion is really a challenge.

Do you have a tutorial available that I could pass on to the upholsterer.  Perhaps some info, website, video that I can pass on, this process you have discribed seems challegening and i would like to ensure the chair turns out.
Regards,

To get a nice rounded edge to a cushion, cut a V-shaped channel out of the sides, spray the channel with adhesive, then press together.  Voila!  A perfect rounded edge every time.  
Use a razor blade to cut the channel.  It will be tougher to do on latex foam because the foam is tougher and more resilient and will tend to compress rather than yield to the razor blade.  (Very soft density urethane foam does the same thing but because it's soft, not tough and resilient.)
Always use a new blade and you may have to change it before you're done.  Foam dulls razor blades very quickly.
You can vary the radius of the curved edge by cutting the V deeper or shallower.  I try to cut it as close to the edge of the side as possible but usually a quarter inch doesn't make much difference.