Apple Mail fails to send mac.com mail

In the Apple Mail app:

• Receiving mail in every account works just fine.
• Sending mail in every account works just fine.
• Receiving email in the mac.com account works just fine.
• Sending email in the mac.com account fails.

The error alert reads

Can’t connect to the account ”Apple”

Unable to verify account name or password.

Except…

• Apple Mail connects to the account “Apple” with no problem when receiving.
• Furthermore, I can send mac.com mail with no problem using the iCloud website — using the same address and password.

So how can it connect and not connect at the same time?

(I’ve read a dozen posts with similar problems, but none of them is the same as my particular issue.)

Anyone have any ideas?