Let me shed some light regarding your concern for your expenses information in QuickBooks Online.
The system only allows you to copy the information from a purchase order to a bill and an estimate to an invoice. The best way to copy the information from your expenses is to manually enter them into the system.
I hear you and realize the convenience of being able to copy the expense information from your invoice transactions to your suppliers account.
Know that our developers are constantly considering new features to be added to the system and cope with your business needs. I'd encourage you to visit our QuickBooks Online Blog site to be updated with our latest news and product road-maps.
On the other hand, know QBO has the functionality to add the billable expenses of your customer's invoice through the use of the billable expense feature. This allows you to copy all the data on the expense and be able to add it to the invoice automatically.
In doing this, you'll need to enable the billable expense feature in the system so you can add them to your invoice. Know that this option is only available to the Plus and Advanced versions of QuickBooks.
To enable it:
Go to Settings ⚙, then select Account and Settings.
Refer to the Expenses tab.
From the Bills and expenses section, select Edit ✎.
Turn on the following:
Show Items table on expense and purchase forms
Track expenses and items by customer.
Make expenses and items billable.
(Optional) Set up the following:
Billable expense tracking
Sales tax charge
Bill payment terms.
Press on Save.
After that, you can now create an expense transaction for your customer and add it to the invoice afterward.
Press on + New.
Select the transaction (Bill, Expense, or Check) you want to create.
Chose the payee.
In the Category column, select the expense account for transaction.
Enter the description and amount of the expense, then select the Billable checkbox.
In the Customer column, select the customer you want to bill for this expense.
Enter or make sure the markup % is correct, then select the Tax checkbox or choose a tax agency if you want to charge tax.
Select Save and close.
Once done, you can now create an invoice and add the expense. Just hit on the Add link on the billable expense that will show up. Please see the reference attached: