Your description is "fridge that uses 7amp at 115V" is necessary information, but not sufficient. That tells you that the inverter involved should be able to provide a peak output of at least 7 amps at 120V.
But you also need to know the average power usage of the fridge in your application. E.g. get a Kill-A-Watt and stick on the fridge to gather some data. Maybe you find the average usage is 2 kWh over 10 hours (a total guess).
Presumably the "solar generator" will have an inverter, solar panel, and battery. The battery needs to be sized for the average usage of the fridge while power is out. The solar panels can be tiny if you are only go to use them to recharge the battery between intermittent outages. But if want them to recharge the battery quickly enough between frequent outages, or to power the fridge during the day with the battery used primarily at night, they need to be much larger.
Cheers, Wayne