Ldap – How to make dovecot and postfix use the same mail directory

I'm trying to configure postfix and dovecot to connect to the same LDAP, and I kind of succeeded. But now, I have some discrepencies.

The reproduction is as:

• I connect to dovecot in IMAP with thunderbird
• I create an email from myself to send to myself
• I use the postfix from the same server with the same user
• I send the email

The results are:

• The sent email is put in the Sent folder.
• But I get no email in my inbox.

Checking on the server:

• The sent email is in the /var/mail/<username>/.Sent/cur/ directory
• The received email is in the /var/mail/<domain>/<username>/new/ directory

I thought I configured the maildir directory both the same way (as in /var/mail/%d/%n), but there must be a problem.

My configuration (external, sorry, couldn't make it in the question. And after 30h (still counting) on those damn configuration files, I'm not really sure which part might impact what…)