Should the imposter whose deception has been proven with evidence be exposed, or should he be covered, and is silence regarding this considered silence about the truth?

Impersonation is forbidden if it leads to belittling the person or causing harm to them, or if the impersonator obtains something they do not deserve, or if it leads to committing a forbidden act. If it is belittling, it is backbiting. If it is harmful, it is forbidden, based on the saying of the Prophet, peace be upon him: "There should be neither harm nor reciprocating harm." If it is for obtaining something one does not deserve, it is injustice. Even if impersonation is free from these prohibitions, it would still be lying and deception, both of which are forbidden in Islamic law. It is obligatory to prevent impersonation if it falls within the prohibited cases.