Can the QB payroll system capture and send to QBO the location field so that the financial statements will show an employee's payroll in the correct location?

Your interest in enhancing the financial statement report in our system is truly commendable, Rodney4.
 

Currently, capturing and sending the location field and assigning a specific location to employees and their respective paychecks is unavailable in QuickBooks Online. As a result, the payroll amount will be categorized as unclassified or unspecified in the Profit and Loss report by Location. 
 

If you think this option needs to be included in the report, you can provide feedback directly to our product engineers. Within your QBO account, navigate to the Gear icon and choose the Feedback option.

Alternatively, you could explore third-party applications that can assist in generating location information, specifically for employees.

Another thing we can do in your QBO account is make use of the Class feature. Once done, you can assign your employee per class. Here's how you could do it.

1. Go to the Gear icon at the top and choose Payroll Settings under Your Company. 
2. Scroll down and click Accounting. 
3. On the Accounting Preferences page, go to the Classes section and select your preferred option.

Afterward, you can create your employee's payroll and run the Profit and Loss by Class.

On the other hand, if you're referring to a work location in your employee's profile, please confirm by letting me know in the comment section. This will allow me to provide you with further relevant information on the topic.

I appreciate your for considering QuickBooks Community to answer your inquiry. I look forward to helping you achieve your goals in any way we can. Bye for now and take care.