Welcome to the Community, @US6.
Let me add some information about how data move from QuickBooks Desktop (QBDT) to QuickBooks Online (QBO).
@Fiat is correct, our system will take care of conversion process. Although, some of your lists and reports may not be converted because of the difference in features. It should include the customer's Phone number.
You may check out this article for common questions: Learn about converting from QuickBooks Desktop to QuickBooks Online.
We'll also make sure your data is accurate once we import it to the online version. But, if you'd like to double check, run a Profit and Loss report or a Balance Sheet report in QBO and QBDT and compare the two.
I've added this link that you can use as a reference once you successfully converted your data: Post conversion checks for getting started with QuickBooks Online.
Feel free to get back and post a comment for any follow-up questions. We'll be here to check on your response. Have a good day!