If you use FBA on Amazon, then you can also opt to have your merchant orders from other marketplaces shipped from your FBA stock instead of stock that you hold yourself, thanks to Amazon's Multi-Channel Fulfillment service
This is only possible if your SKUs on your other marketplaces are the same as your FBA SKUs, and you have stock of the item(s) with FBA.
To enable this option, first navigate to Settings > Channel Management > Sales Channels, then click the Manage button on your Amazon account:
Under the Miscellaneous section, toggle the "Enable MCF via FBA" option to ON:
Once this setting is enabled, you can navigate to your orders page and select the merchant orders that you want to send to FBA, then click the Ship button:
If you have FBA and a courier connected, you may be given a drop-down menu to select which service you want to ship with, so in this case, select Amazon FBA to send the order through to your FBA account, rather than creating a courier label.
Once the order is submitted to FBA, the order status will automatically update in ChannelGrabber once FBA have dispatched the order, just as if you had dispatched it yourself.