Given the level of competence that clients seem to be showing these days, I'd insist to have him log into his account with you (here in CA it's coveredca.com) and see for yourself that there are no CY tax forms.

Other than that, I'd extend the return, get a signed 8821 and call the IRS Practitioner Priority line to see what they can tell you, if anything.  It won't be on a wage & income transcript unfortunately, even when they do get released in a month or two.

If you paper file, I'd put an 8275 disclosure in there saying the reject you got and where you looked, seeing no 1095-A.

Good luck!