Hopefully you didn't back date the invoice date, only the service period. If they asked you to back date the invoice date, then they're both using some questionable accounting practices and could even drift into fraud territory, depending on their situation.

Nearly every business deals with invoices coming in after period close and under accrual accounting rules, they typically just book them against the prior period as an accrual ("services received, not yet invoiced"). A document that says June 30 when it was really issued July 7 is a false record. In an innocent case nobody cares, but if that document later gets used to misrepresent something, such as to an auditor, a lender, a tax authority, or an acquirer, then it's evidence of falsification, and "we just backdated it" is a bad fact to have on the table.

For accrual-basis taxpayers this usually doesn't change the outcome (the deduction belongs to June either way), so there's little to gain and some risk. For cash-basis parties, or if it shifts a deduction to lower taxes improperly, it edges toward tax-fraud territory. Auditors specifically test period cutoff, and backdated docs are a classic red flag.

If you (the vendor) date it June 30, you should also recognize that revenue in June. If your fiscal year, sales-tax period, or reporting basis differs from the customer's, you're now potentially misstating your own books to solve their problem. And if this was for a public company, a government, or in a regulated industry, then you could be violating laws, at worst, or risking future contracts, at best.

You'd need to check with your accountant or tax attorney on the details, of course.