[email] Should I use the Reply-To header when sending emails as a service to others?

You may want to consider placing the customer's name in the From header and your address in the Sender header:

From: Company A <[email protected]>
Sender: [email protected]

Most mailers will render this as "From [email protected] on behalf of Company A", which is accurate. And then a Reply-To of Company A's address won't seem out of sorts.

From RFC 5322:

The "From:" field specifies the author(s) of the message, that is, the mailbox(es) of the person(s) or system(s) responsible for the writing of the message. The "Sender:" field specifies the mailbox of the agent responsible for the actual transmission of the message. For example, if a secretary were to send a message for another person, the mailbox of the secretary would appear in the "Sender:" field and the mailbox of the actual author would appear in the "From:" field.