Kristi Noem allegedly created a fake press release using doctored State Department letterhead to explain why she was exiting her special envoy role after getting fired as DHS secretary ... this according to reports.

After the State Department announced her exit, Noem shared a press release on State Department letterhead, saying ... "The Special Envoy to the Shield of the Americas role was always a six-month appointment. Secretary Noem remains at the State Department as a Senior Advisor."

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The issue? Sources at the State Department say it was not an official release ... and that the letterhead was fabricated.

A person familiar with the situation told Politico ... "This was not a press release put out by the State Department. Noem went rogue and created a fake letterhead to post on X."

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An official confirmed the same to CBS News' Olivia Gazis ... who wrote ... "A State Department official confirmed that a statement posted by Kristi Noem to her official envoy account and personal X account was created using fabricated State Department letterhead and was not an official department press release."

We've reached out to the State Department and Kristi for comment ... so far, no word back.