Mailgun can't prevent an email client from displaying the "On Behalf Of" notation when the domains in the Sender and From fields don't match. To eliminate this notation, the same domain should be used in both fields.
Additionally, message headers can be used to provide more information about the sender and the message.
This information can be used to verify the authenticity of the message and the sender.
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It is important to understand that there is no way for Mailgun to prevent an email client from displaying the "On Behalf Of" notation as long as the domains contained in the Sender and From fields don't match. However, ensuring the exact same domain is used in both fields will eliminate the "On Behalf Of" notation.
Why Do I See "On Behalf Of" in My Email? – Mailgun Help Center
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Routes — Mailgun API documentation
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Introduction — Mailgun API documentation
However, there are some good clues. Mailgun provides DKIM and SPF verification for incoming mail, which is shown in the MIME headers once spam filtering is ...
FAQ — Mailgun API documentation