As 'ego2dot0' said above, you don't need any MDA filters (sieve etc.) to do this. It can be done using Postfix alone, although it took me a while to figure out how to do it.
You have to use sender_bcc_maps AND virtual_mailbox_maps features together.
You have to use a virtual domain dedicated specially for copies to self. If your actual domain is "your.domain.tld", you can use eg. subdomain "copyself.your.domain.tld". This subdomain does not have to actually exist, ie. be defined in the DNS (moreover, it's better that it isn't defined, so nobody accidentally sends mail to it from outside). It is a purely virtual domain that is recognized only by Postfix.
1) Configure sender_bcc_maps to BCC mail coming from user@your.domain.tld to user@copyself.your.domain.tld. You can do it for only a few selected users using a regular "hash" type map, or you can do it for all users at once using PCRE type map and regular expressions.
2) You have to define your virtual domain in virtual_mailbox_domains, like this:
virtual_mailbox_domains=copyself.your.domain.tld
3) Configure virtual_mailbox_maps so that the destination mailbox for address "user@copyself.your.domain.tld" is the actual "Sent" mailbox of the user "user". For example (assumed that you are using regular system users and Maildir format - like in my case) the path to "Sent" mailbox for user "user" will be "/home/user/Maildir/.Sent". So, you can define common part of the path as virtual_mailbox_base, eg.
virtual_mailbox_base=/home
and then in the virtual mailbox map enter the rest of the path like this:
user@copyself.your.domain.tld user/Maildir/.Sent/
(the trailing / is important to indicate the Maildir format).
Again, you can use PCRE type map to do this for all users.
4) To properly save mail to the mailbox, Postfix need to also know the proper UID and GID for the particular user, so you have to use virtual_uid_maps and virtual_gid_maps parameters as well. If you are using virtual users, it's probably enough to define "static" type maps specifying a single UID and GID of the system user that owns all the virtual mailboxes. However, if you are using system users like me, you need the proper actual UID and GID for any user. If you have only a few users, you can use a regular "hash" type map, with entries like these:
user@copyself.your.domain.tld 2001
or you can try to setup a pipeline with "pipemap" map type, that uses some PCRE maps and "unix:passwd.byname" map to obtain the UIDs and GIDs for all users (I haven't done this part, as my Postfix installation is compiled without "pipemap" type support).
So to sum everything up, use something like this:
In /etc/postfix/main.cf file, add the following lines:
sender_bcc_maps=hash:/etc/postfix/sender_bcc
virtual_mailbox_domains=copyself.your.domain.tld
virtual_mailbox_base=/home
virtual_mailbox_maps=hash:/etc/postfix/copyself
virtual_uid_maps=hash:/etc/postfix/copyself_uids
virtual_gid_maps=hash:/etc/postfix/copyself_gids
/etc/postfix/sender_bcc contains a bunch of lines like:
user@your.domain.tld user@copyself.your.domain.tld
/etc/postfix/copyself contains - respectively - lines like:
user@copyself.your.domain.tld user/Maildir/.Sent/
/etc/postfix/copyself_uids and /etc/postfix/copyself_gids contain - respectively - lines like:
user@copyself.your.domain.tld 2001
I have done this on my server and it works great for me.