“about his tax return”
A tax return is a document submitted to the tax authorities. In the United States, people report the previous year's income and deductions, generally by spring. Preparing and submitting it is called filing a tax return. It corresponds to Japan's annual individual tax-filing process.
“business expense list”
A business expense is a cost incurred for work that may be deductible from income for tax purposes. The accountant therefore checks whether personal spending, such as coffee for Frank himself, belongs on the list.
“Then we can check what qualifies.”
Qualify means to meet the relevant conditions or be eligible. In this tax conversation, it means to be accepted as a business expense or eligible for a deduction. The accountant will check which costs can be claimed.