How to share iMessage

You can forward messages:

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Note that if you try to forward them to the email address that you use for your Apple ID, they will just show up in Messages, not in your email.

Or, do you mean you want to share messages with your ex?

Yes, it's possible to forward individual messages to an email address. I provided a link on how to do it.

No, it's not possible to automatically forward all messages to an email address. Apple never said that they offered that feature.

If you explain in more detail exactly what you're trying to accomplish, we could stop guessing at what you mean and perhaps give you a better answer.

Bomiboll wrote:

The instructions says: On your Mac, open Messages, choose Messages > Preferences, then click iMessage

But I see no iMessage there

And as for the iPhone, Settings > Messages > Text Message Forwarding.

It is set to forwarding But it does not forward at all.

I would like to forward to any email

What you're talking about is not forwarding a message to your email. What it does is enable you to send and receive SMS messages from other devices that share an Apple ID with your phone. It doesn't forward SMS messages or iMessages to your email.

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

See “Set up iMessage” here.

Use Messages with your Mac - Apple Support