Can we use the search function to search for a two years past transaction?

Yes, @userlm. Let me give more details about the Search tab on the upper left side of QuickBooks Online.

If you're talking about the Magnifying glass above, yes, you are right. We can find the cheque on the said tab. Nonetheless, QuickBooks show a limited list of possible results.

Furthermore, if you want to locate the specific transaction, we can directly type the transaction number, and QuickBooks will let it appear on the screen.

Moreover, if you're looking for an older transaction you can also utilize the Advance Search. This way, you can filter the date and the transaction type. 

See the Illustration below for your guide:

In QuickBooks, there are two ways to display your account: Business View and Accountant View. If you want to understand the differences of both view: Switch between Business and Accountant view in QuickBooks Online.

Do you want to know great features in QuickBooks Online? Please notify me again. I'm always ready to back you up.