Thanks for all the replies.
No outlets in the transfer switches unfortunately.
I wondered if the installer had removed the outlet but couldn't think of any reason why he would. Now I get it, that is how he wired the inverter into the house system. Mystery solved :)
The inverter is all hard wired. The converter is still connected to the battery. So I think I will just run a new AC line to give me somewhere to plug the converter in. As both the inverter and converter are connected to the battery I just need to make sure I only run one at a time.