The Shelby cycle history page
does refer to Shelby making bicycles for the Chicago Cycle Supply Co.
Shelby Steel Tube Co. 1891 Lozier-Yost Seamless Tube Works, then The Shelby Steel Tube Co. formed Lozier and Yost and bring technology back from England Jonas Feighner and Capt. D.L. Cockley raised…
shelbycyclehistory.org
It also shows various fits and starts of the company, and even a Mead (see sprocket) connection.
Maybe the “A” serial numbers might start in 1923?
Preserving the memory of the bicycle industries in Shelby, Ohio
shelbycyclehistory.org
Or was it like 1925-A, and skipping some letters such as “L” and maybe “I”?