To do this, you need to map your Magento Payment Methods to payment methods stored in Linnworks.

First, you need create new Linnworks Payment methods:

• Go to Open Orders > New Order
• Click the magnifying glass button next to the Payment Method
• Click the Add New to create a new method and save it

This will store a Linnworks Payment Method. To map these to Magento payment methods, you will need to 

• Go to Settings > Channel Integration > Magento - Edit channel payment ($)
• Map your Magento Payment Methods to your Linnworks payment methods

Any new orders downloaded from Magento will have the correct payment method displayed on them.