It means "I hope you will in good health (well) at the time you receive this letter".
Yes, it sounds outdated.
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It was the use of 'may', in particular, that made the expression inthe original query seem outdated to me. These other suggested variations seem a little less so, but with no offence to anyone, I find it hard to believe that a lot of younger native speakers will continue to write this way. (Will they even write at all, or just send cryptic text messages?)
"I hope my email finds you all very well?"
"I shall" was also often used by that person.
People are waiting to help.
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