Answering myself (not yet implemented, but I hope it will work):
Using sieve  extprograms extension and global "after" script, I can read .dovecot.sieve.log into a sieve variable 'log_content' if this log is not empty. I hope this log will be written before "after" script is called, but will check if it is true.
Then using sieve "notify" action with mailto:${user_mailaddress}?body=${log_content}"
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  Sergey.

On Thu, Feb 1, 2018 at 5:01 PM, Sergey Ivanov <seriv@cs.umd.edu> wrote:
Hi,
What are the recommended ways to give access to their .dovecot.sieve.log messages to the users?
I am thinking about placing this file into users Maildir/new, or piping to dovecot-lda.

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  Regards,
  Sergey Ivanov