You are misunderstanding the rule.  Accrual accounting recognizes revenue when it is earned.  Preparing an invoice at a later date does not entitle you to defer the revenue.  The amount was known once the service was performed.  When you or your staff get around to sending the invoice is irrelevant for accrual accounting.  

As a former financial statement auditor, I can tell you auditors specifically test for this (cut-off testing & revenue recognition) by reviewing Jan and Feb invoices to ensure revenue was recognized in the proper period.  

In my case, a retainer was received in Nov, the service was performed in Dec, and the invoice was prepared in Jan. 2022.  The revenue absolutely has to be recorded in 2021 (using the accrual method) because that is when it was earned.

~ Shay (a CPA with over 15 yrs experience)