[unix] Change the "From:" address in Unix "mail"

None of the above solutions are working for me...

#!/bin/bash

# Message
echo "My message" > message.txt

# Mail
subject="Test"
mail_header="From: John Smith <[email protected]>"
recipients="[email protected]"

#######################################################################
cat message.txt | mail -s "$subject" -a "$mail_header" -t "$recipients"