Sieve-Example:Notify

Send a notification email to another mailbox when the mailbox gets an email:

Roundcube screenshot for sending a notification email to another address

If you can edit the sieve filter manually, then you can also get the Sender and add that to the subject line:

# rule:[notify]
if header :matches "Subject" "*"
{
	set "subject" "${1}";
}

if header :matches "From" "*"
{
	set "from" "${1}";
}
notify :importance "2" :message "[Notification] ${from}: ${subject}" "mailto:someone@example.com";

This sets a variable of the subject, and then sends an email to another mailbox using the subject line.