No there's no filter in them stock at all but there's a bunch out there to fit a 3/8 hose. The booster has a check valve that's almost a pencil point that if it gets stuck can either give all the pressure or take it away.Yeah, I was going to replace the connector too, just in case.
As for the hydraulics, I just replaced what was in the truck. I didn't add anything else. I don't see a filter in the TMs, so it hadn't occurred to me.
Are you suggested trying to pull out as much power steering fluid as I can, and try dextron in it? It can't hurt, I guess. If the boost has gone bad, I can't really make it any worse...
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