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Prepaid Rent (Accrual Based Accounting)
Your account entries are generally correct, but do note that the last transaction is a mixture of the balance sheet and income statement.  If Quickbooks doesn't do this automatically then the expense must be manually removed from the balance sheet. The expense should be recognized on the balance sheet and income statement when it accrues, and it accrues when the prepaid rent is extinguished when consumed by the landlord, so that is when the second entry in your question should be booked. The cash flow statement will reflect all of these cash transactions immediately.