No need for CREATE TABLE since there are SELECT INTO statements

Try this:
SELECT UserAccount, AccountType, BillingAccountKey, BillingCode, [Rank]
FROM
(
    SELECT
        UserAccount = UA.UserAccounts,
        UA.AccountType,
        UA.BillingAccountKey,
        BR.BillingCode,
        BR.[Rank],
        RowNum = ROW_NUMBER() OVER(PARTITION BY UA.UserAccounts ORDER BY BR.[Rank] DESC)
    FROM #UserAccount UA
    INNER JOIN #BillingTransactions BT
        ON BT.BillingAccountKey = UA.BillingAccountKey
    INNER JOIN #BillingCodeRank BR
        ON BR.BillingCode = BT.BillingCode
    WHERE UA.AccountType = 'O'
) SUB
WHERE SUB.RowNum = 1
ORDER BY UserAccount