For the record, the expansion "... his" is considered "folk etymology": a reanalysis from the Early Modern English period in the language's history. Notice for example how it doesn't make sense for feminine words: "Mary's house".

In fact, the possessive "'s" is a leftover from Old English, where the inflectional suffix "es" marked the genitive case.

Yeah it's a mnemonic device, nonetheless quite useful to explain the rule.

Thanks!