Can an equipment invoice issued on behalf of the IRS be proved to be your own?

Can.

The invoice from the tax office has the name of the company, the tax ID, the address and the cell phone number, all of which can prove that the invoice is their own.

The invoice has the word "open" on it, which means that the enterprise or individual has not applied for the tax registration certificate, and has no qualification for developing invoices, so it can only look for someone else to open it, and pay the tax on behalf of the enterprise or individual.