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
mail.message table. It also keeps original values to allow to move
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.
Please note, that after uninstalling the module, all infromation about original location of moved messages will be lost.