Depending on what the Imp rating of that 50w panel it may be a little small for a 40Ah battery. You need about 1/10th the Ah rating to charge an FLA type battery. For the 40Ah that would be 4 amps. You can get away with 1/12th the Ah rating or ~ 3.33amp of charging but run the risk of not getting the battery charged back to 100% each day.
Inverter to Battery
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