Can Cart2Cart migrate invoices?

Yes, Cart2Cart provides migration of invoices within Magento and PrestaShop as an additional option. Credit memos and shipments are also migrated, but within Magento stores only.

Note for Magento users:

Cart2Cart allows to move carriers along with shipments too. Nonetheless, if the carriers are not installed on your Target store, they’ll be displayed as following:

As for other migration pairs, Cart2Cart moves orders exclusively. However, you target shopping cart may generate invoices automatically, if such an function available. In another case, you can generate invoices manually after migration is finished.