What is the best way to migrate payslips from an old accounting system to Quickbook?

Welcome to the Community and thank you for choosing our service, @johnidy.

Depending on the accounting system you're using, you may or may not import historical payroll transactions into QuickBooks. If this is the case, you can just enter an opening balance per employee when getting started with payroll in QuickBooks Online.

If you're using Xero or MYOB, you can refer to this KeyPay site for more information about the integration: https://www.keypay.com.au/feature/integration.

You can also refer to this guide: Migrating your payroll from the different accounting systems.

I've got your back and will be here should you need additional assistance. Take care. 

You can import your payroll CSV file into QBO as JE using an importer tool

https://transactionpro.grsm.io/qbo

https://partners.saasant.com/affiliate/idevaffiliate.php?id=5051_2

Hope it helps.