The Fine Things are Always Hand Made
Yes - is repairable. There are 2 field coils. Strange they appear to be shorted to each other.
I have had two AW- 15 speakers with bad B+ fields and had both rewound some years ago. The speaker is a special Jensen and well worth repairing. My cones were also brittle and dried out, so got new cones as well.
Dismount the pedestal and then work off the heavy cast rear cover to access the field coils. Be careful of the voice coil. The two field coils are side by side on a common form. Observe polarity and direction of the windings you - don't want the two coil fields fighting each other.
Perhaps you will be lucky and find the problem is the leads to the actual field coils and can just repair or replace the leads.
The speaker you have is desirable and repairable, to quote Dave, remove the heavy cast cover,
the field coil is more or less a smoothing choke for the power supply and a transformer for the 2A3 bias, hopefully the wires are damaged and not the windings, as sometimes the old cloth covered wire can rot depending on how the radio has been stored in the past.
The coil in my allwave 15 was covered in tar, but ok.
luckily it was a rebuild with new voice coil and cone, the most difficult part is putting the speaker back together, the voice coil will have to be centered on the pole piece otherwise it will rub and sound terrible, use some shim between the inside of the voice coil and the pole piece on assembly, this can be thin plastic or card,
see my article on making a field coil speaker as most of the info applies to your problem
Thank you both for your advice sounds like a wintertime project. Norman W