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.
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.
If you send me unsolicited commercial messages, I'm gonna feel no compunction about publicizing that you're a spammer.