Welcome to the Community family, @Steiskal.

With QuickBooks, you can easily e-file your 1096's form along with your 1099's instead of filing manually. However, once you've filed the form, it’ll go along with the IRS. 

To print your 1096’s, you’ll need to contact the IRS and get a copy from there.

In case you need to print your 1099’s in the future, see this link for your reference: How do I print my 1099 forms?

Let me know if you have other queries printing forms in QuickBooks. It’s always my pleasure to lend a helping hand. Have a good one and keep safe.