Only at the most primitive level of morality. Over that basic layer, I'd still consider how the publication of the message may affect the other person.
For example: Do you think it's morally OK to publish nudes that your partner sends you? I don't think it should be illegal, but only a massive asshole would publish their (ex) partner's nudes.
Morally, to each their own. But legally it certainly depends. In France you can't for private conversations, for example. I don't know if this one would qualify.
In fact no. Once I send you a message it’s neither yours or mine, it’s owned by the platform. Thus if the platform does not allow for « sharing » without consent you must follow their instructions.
Also if you believe privacy is a right, you should ask that person before sharing this digital content he created that has hid identity in it, otherwise you should hide it.
For a paper letter it’s obviously different, once you received it it’s obviously yours.
The object may be yours. Copyright in the contents unless specifically assigned elsewhere (in many service agreements a grant but not an assignment is made to the service operator), remains with the author.
Fair-use affirmative defence (under US law), fair dealing (UK),or equivalents elsewhere, may apply. Infringement claims, if any, would rest on thin grounds. Under the specific circumstances here, privacy claims likewise.
There is no copyright protection in the fact of communication. Nor in the details of who did so.
Generally I'd argue for a legitimate public interest in sharing the communication in cases such as this.
Only at the most primitive level of morality. Over that basic layer, I'd still consider how the publication of the message may affect the other person.
For example: Do you think it's morally OK to publish nudes that your partner sends you? I don't think it should be illegal, but only a massive asshole would publish their (ex) partner's nudes.