The thingy you showed is (I think) a device to limit fluid flow in one direction (down). It's there to limit the speed of drop in case of a hose rupture also to keep a max weight load from coming down uncontrolled. On the 4000 hd industrials it's a cup in a cylinder.
The pump should be about 25gpm at 1700 rpm. (From memory)
Here's what I would do in your place;
1- remove the hose from the cylinder (end in a clean bucket) and verify there is strong flow. Push out a couple gallons. That will determine if they control is good or not. It should dump 2 gallons in about 12 seconds at idle (550 rpm). Kill the engine at 2 gal.
If the flow is restricted, take the control valve segments apart and find out why. I suspect the control valve. It uses o-rings and square edge rings. Common and easy to find in a hydraulic store (brick or digital). Look online at fnh website for the part breakdown. Look at the check ball too. Could be the issue.
2- inspect the fluid for water (milky), particles, chunks of seals or packing. The debris will help id what failed. Pour the fluid back through a funnel, filter debris with a clean old tshirt.
3- inspect the cylinder inlet for blockage.
4- take apart the cylinder and repack / reseal. If there is debris, you should probably take apart the rest of the cylinders or the will probably also fail. And the tank and lines should be flushed / cleaned. Pita!