The problem of the last blog article about sending emails usually affects one account on one device. 

But sometimes it's not possible to send emails at all: all email clients, all devices, and most or all accounts. This usually occurs at 2 situations:

  1. You got a new router.
  2. You changed hosting companies, your domain or the hosting company changed the main or internally used domain.

Mr. Spammer is a clever guy. He doesn't want to pay for sending emails and lets other people to that for him. Therefore, he captures other peoples computers and has them sending emails for him. To prohibit that the router can have a whitelist of domains which are allowed to send emails. Usually, you don't notice the feature. Until you get a new router or your hosting information changes.

I have done both myself. The new router is kind of obvious. But at one time my hosting company changed my plan and with the new plan the main domain changed from mothsoftware.de to an internal domain. And I wasn't able to send emails for Moth Software. Of course, I have multiple accounts for iCloud and Gmail.

Obviously, the settings will be different for each router. For my German Telekom router the feature is called "E-mail abuse detection":

Email abuse detection for Telekom routers

The router has a list of already approved SMTP servers like Gmail or iCloud. Click on the plus button with the label "Add further e-mail server" to add a new SMTP server.