Is it permissible for medical clinics to create two invoices to inflate the amount in order to cover losses resulting from their dealings with insurance companies that deduct high amounts, and does the physician bear sin for signing the second invoice?

If it is permissible to take from one who has wronged, then there is no harm for the doctor in signing the necessary papers for that. However, clinics are not compelled to deal with insurance companies or grant them discounts; rather, they do so to attract customers and increase profits. Forgery — including forging invoices — is consuming wealth unjustly and is among the greatest sins, as the Prophet, peace and blessings be upon him, said: "Shall I not inform you of the greatest of the great sins? Associating partners with Allah, disobedience to parents, and indeed, false speech and false testimony." Based on this, it is not permissible for the doctor to sign forged invoices.