Impeachment is a political act of the Legislative Branch.
Criminal acts are prosecuted by the Judicial Branch.
Document forgery, fraud, etc, are criminal acts. A person committing these acts is liable for prosecution; holding Office is no shield, these are not Official acts which would be shielded.
Conviction and imprisonment would be insurmountable disabilities necessitating impeachment.
Of course these particular criminal acts would mean that there is no President and therefore impeachment is impossible. The Constitution demands that “No Person except a natural born Citizen... shall be eligible to the Office of President”, it can not then require that an ineligible person be impeached. To contend otherwise would negate Article II’s imperative that “No Person except a natural born Citizen... be eligible”. A person who is not President can not be impeached. Not only is it illogical to impeach an ineligible person, such a reading is an invalid construction.
Unless, of course, one has pigmentation immunity.