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Hello and good day. A couple things;
1) What is the total output of the generator?
2) The 220V output plug on the generator, how many amps is it rated for?
3) Can you hard-wire off the output?
3) Is it a straight 220V 3-wire? 2 hots and a ground, or a 4-wire 2 hots, a neutral and a ground.
4) Your total demand load in the cabin will determine what you need to run for a service, but if you want to supply 100A at that distance, if you buried a cable you would want to go #2AWG copper or larger if aluminum.
5) You would need a transfer switch to switch between solar and genset for your power in the shed
You would just need to make a transfer system with the panel, genset, and the solar. So you could switch which power source you have supplying the panel and to prevent back feeding. If you think you might be hooked up to the grid at some point, you want to make sure your panel in the shed has a main breaker for whatever amp service you might end up getting. Or you will have to make the necessary changes later on, whichever.
But first you want to see if you have a 120/240 output receptacle from your generator and what amperage