Wood burner back boiler gravity circuit problem

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From memory (I'll check when I get chance) the installation manual says you can use 3 or 4 connections. Is there a benefit to using the injector tee and only 3 connections? Would it help the gravity circuit? The original stove didn't have one, it also had 4 connections.

It will not help the gravity circuit, when fire working solely on gravity if an injector tee 3 pipe to 4 pipe is used, nor is its purpose.
But it will help the gravity circuit to keep circulating and prevent reverse circulation in the gravity pipes if an injector tee is used.
When the pumped 2 pipe circuit pumps water it tends to rob the 2 gravity pipes of circulation and reverse the gravity circulation on 4 pipes linked directly to fire type installs.
Your gravity circuit should therefore be capable of circulating normally when pump isn't on, even if no injector tee is fitted.