Which of the following transactions should be recorded in the accounting system?

The transaction involving the plumber fixing a leak and sending an invoice in June should be recorded in the accounting system because the service has already been performed. In accounting, it is essential to record transactions when they occur, regardless of when payment is made or invoiced. This aligns with the accrual basis of accounting, which recognizes revenues and expenses when they are earned or incurred, rather than when the cash is exchanged.

Recording this transaction ensures that the financial records accurately reflect the organization's financial position and performance at that point in time. It highlights a liability that will need to be settled once the invoice is received and promotes clear tracking of expenses, which is critical for budgeting and financial analysis.

In contrast, the other options represent situations where no transaction has yet occurred in terms of a financial exchange or obligation that has been realized and thus would not be recorded immediately.