Numbering possibly continues from Blue Beetle (Fox, 1939 series) #57 (July 1948), skipping #58 and #59, with Western Killers #60 (September 1948). While unconfirmed and somewhat questionable due to the skipped numbers, no other currently-published Fox series had even reached issue #20 at this time. There is at least one confirmed instance (Romeo Tubbs) of a Fox numbering sequence going off by one (although in the other direction, creating a duplicate number) when changing series.
Note that Blue Beetle also continues its own numbering with #58 (April 1950) nearly two years later, a type of continuation which was also done with My Secret Life, the numbering that was continued into Romeo Tubbs, although it's worth noting that the My Secret Life / Romeo Tubbs numbering happened much later and the re-continued numbering was done somewhat later, in 1950-51.
Numbering continues in My True Love Thrilling Confession Stories (Fox, 1949 series).