Is it unlawful for a household electrician to take a check from the bank funding the house in his name after purchasing the materials and completing the wiring work, then sending the invoice to the bank, knowing that he sometimes estimates the materials before finishing the work and increases the amount on the invoice to give the excess to the homeowner to purchase other materials?

It is permissible to combine ijarah (leasing/contracting) and wakalah (agency/power of attorney) such that the employer contracts with you to perform the work and authorizes you to purchase the necessary supplies. However, if you purchase the supplies from yourself, the preponderant opinion is that it is not permissible unless with the employer's permission. There is no harm in issuing the invoice before the completion of the work and estimating the value of the remaining supplies, provided that any excess is returned to the employer, as long as you do so without intending to inflate the cost and based on your own judgment. There is also no harm in you receiving the invoice amount from the bank, even if the financing transaction between the employer and the bank is prohibited (e.g., an interest-based loan), because the prohibition of the loan pertains to the liability of its borrower, not to the money itself.