My understanding (and this is where it stops) is that the "K" denotes an Alnico motor vs Ferrite for the "E" serie. The K151 was most likely a driver for electric organ instruments.
Can a 2245h cone kit be fitted to a K151 basket? I know that the e155 basket can receive a 2245h cone kit.
EDIT - Just found a tech info by Mr SubWoof
"there were 3 versions of the 18" ferrite frames and all will take the 2240,2245 or E155 kits.
The older K151 and the rare E151 had a much different looking frame and I would not use them due to insufficient clearance for cone travel."
So... Not suitable for a 2245h recone.
Lee