Odoo has a good integration with emails. It allows to have a discussion with a customer attached to some record (task, lead, invoice etc.).

In the main, your customer don't know about this and can send emails (e.g. about a task) to your personal alias (e.g. admin@yourcompany). It could not be a problem, if you work on task alone. But if you need to share mail to colleagues, it's better to move (attach) mail to task form. I've made module mail_move_message to do it.

Technically, the module update fields res_id and model of mail.message table. It also keeps original values to allow to move everything back.

A usage guide with screenshots can be found here: https://apps.odoo.com/apps/modules/8.0/mail\_move\_message/

It's not mentioned in module's description, but if you move a message, then all messages in a thread below the message would also be moved to a new location.

Repository: https://github.com/yelizariev/addons-yelizariev/tree/8.0/mail\_move\_message