Thanks again for helping me out.
Changing the password allowed me to enter phpLDAPadmin, but to the left I got the following message:
Logged in as: cn=Manager,dc=example,dc=com
dc=example,dc=com
This base cannot be created with PLA.
So I could not search for any users.
Tried the ldapadd command you suggested, got the following result:
ldap_bind: Server is unwilling to perform (53)
additional info: unauthenticated bind (DN with no password) disallowed
So I added a -W, in order to get asked for a password, so the full command looked like this:
sudo ldapadd -x -D 'cn=Manager,dc=example,dc=com' -W -f /home/MyUser/iRedMail-0.8.5/conf/ldap_init.ldif
And now it works!
phpLDAPadmin is showing the full tree to the left, Manager password is restored to something more secure and iRedAdmin works fine!
Again, thanks a lot for your help!
Btw, saw the comment about Mailpile above, it definitely looks interesting.