how to test the 4l80e oil cooler circuit properly

Hi guys,
I swapped a '98 4l80e in my 1984 6.2l Suburban.
I routed new cooler lines to the Radiator , then to an aux cooler, then back in direction to the Tranny thru an aux hydraulic filter with built in temp sensor and now back into tranny.
Last week I did the first test ride to program my tci tcu.
On my Laptop I could see a tranny-oil-temperatur about 65°C but at my aux temp gauge I couldn't see any temperatur.
First I thought the temp sensor wasn't working.
But, back in my garage I touched the tranny pan and it was warm, approx those 65°C, but the left circuit was cold!
Now I disconnected the outcoming line, started the engine and a strong stream came out. Then I disconnected the incoming line direct at the tranny and a slightly weaker stream came out.
So, I think the circuit is okay as far as possible.
But, now to my question: how could I test or determine that the oil is going back into my tranny as it should??
I figured out that the lube line is going back into the tranny, back to the pump body and via a second line, the lube pipe to the back of the tranny .
What do you think, is it possible that those two lines are somehow plugged or so?
The tranny worked fine at the test drive. But I bought the tranny used. The preowner said, it worked all fine.
I'm just sorrowed, because the whole outer circuit was cold while the tranny was warm.
I hope somebody has some ideas!
Greetings Marco