Vtg Stoneware "A Mug for A Mug" Shaving Mug Champrel from the 1940"s?

Description

We have had this mug for several years and I could never figure it out and then recently I saw one that clearly showed the phrase "A Mug for a Mug" and we had a light bulb moment. The mug is not marked "Champrel", however, we did see an ad in a 1945 Sears catalog that had one just like it. There is a name and some initials on the  on the bottom and we could not find any information on what those might be.
The mug is 2 3/4" tall and the top is 3" in diameter.
As sturdy as this mug is, it could also be used as an actual drinking mug as long as you were careful not to remove all of the lettering and picture when washing it.