What 'is' is
A former colleague is adamant that he's must be a contraction for he is and may never be used for he has. Presumably this is to avoid ambiguity. And this distinction has apparently been elevated in various places to the status of a Rule.
But oddly, Garner’s Modern American Usage, Merriam-Webster’s Dictionary of English Usage, the New Fowler’s and Bernstein’s Careful Writer do not address the issue, at least as far as I could tell from a hurried check. The formidable Bill Walsh writes in The Elephants of Style that “many people are quite uptight about the fact that ’s can stand for either is or has. Unless that dual role could somehow cause confusion, don’t worry about it.”
It seems unlikely that anyone would understand “She’s going to work” as “She has going to work” or “He’s been on the phone for an hours” as “He is been on the phone for an hour.”
Focusing on a potential confusion that will almost never occur reflects the manufacture of unnecessary “rules” that bedevils the business — wasting editors’ time on gossamer distinctions instead of genuine ambiguities and outright errors. If you object to he’s for he has on personal, aesthetic reasons, don’t use it. But don’t compel others to endorse your preference.
(I myself am a reformed sinner, having spent untold keystrokes on this unnecessary fussiness. But no more.)
In a broader context, though, there is reason to take some care in using contractions. While they are still forbidden in most academic work and other formal writing, they have become increasingly acceptable in the informal, conversational tone of most journalism and popular writing.
But even there, as Bryan Garner advises, it is best to stick with the most common contractions unless you are trying to reproduce speech. So, he says, avoid I’d’ve, it’d, she’d’ve, should’ve, there’re, who’re, and would’ve.