Not true. Sears very well did indeed sell bicycles in 1945, 1946 and 1947. There were indeed model numbers for those years as well. Yes. My late friend, Viktor Schreckengost (Sears' head bicycle designer) confirmed this fact for me. We have the literature, of course... including individual Owner's Manuals.
It is a fallacy of this hobby (largely based on Xerox-copy-from-catalogue "books") that all Sears Elgin, J.C. Higgins, etc. bicycles were pictured in consumer mail-order catalogues. They weren't. The hobby should drop this notion because it is sadly mistaken.
Also, not all numbers on Sears bicycles with "50" prefixes are "serial numbers"... most are model numbers (and yes, model numbers usually indicated the manufacturer). Not the same as a serial number. Two different things.
Leon Dixon
National Bicycle History Archive of America
(NBHAA.com)