Transmission cooler install:
Step 1: Remove front bumper from car. 
The photos here show the engine out of the car, but you can do this just the same with the engine in the car.
Step 2: Install the
AER-FBM5013 -6an adapter fittings into the holes in the trans cooler.
USE THREAD SEALANT.
Step 3: Install trans cooler as shown below.
These are the holes I am using to mount the trans cooler just below the hood latch. They're threaded already (but unused), and it seemed like the ideal spot to put the trans cooler as it will see airflow from both the upper grille, and the lower grille.
One bolt in, as you can see, the holes that come in the cooler dont necessarily line up with these two holes on the chassis.
That's fine, just drill a hole in the mounting flange in the right spot (cooler metal is very soft and easy to drill)
And mounted with both bolts
What it looks like from a few feet back, you can how it gets airflow from the upper grille, and really appreciate just how big it is.
Assembling the -6 AN hose. A lot of people are intimidated by stainless braid and making hoses. It is
VERY simple. The fittings unscrew, as seen here. Slide the braided part into the fitting end, as far as it will go.
Use silicone lube/grease (same grease you use on suspension parts) to assist in sliding the hose into the -AN fitting end. also use grease on the threads, and other part of the fitting. The grease helps everything go together nicely, and will make sure you don't gall any of the threads on the fittings.
The -AN end on the hose
Once you get the hose all the way into the end, you screw the male end into the end. You'll need two wrenches (3/4 and 11/16, or 3/4 and 3/4 depending on which fitting you're doing). Screw it in until it is flush and tight.
Tada, you've done your first end
At this point, you'll have one -AN fitting on the hose, and 20 feet of hose hanging off of it. (Well, that's how I did it because I had to start from scratch, but you can save time and use my measurements if you'd like.)
I put the end onto the far side of the trans cooler, with all the hose hanging off of it, so I could run the line, and see where I needed to cut it
A view from the bottom side of the trans cooler
I sat the radiator in place, to see how I could possible run the hose to the back of the car. Thankfully, there's a cutout in the lower radiator shroud which just happens to be the PERFECT size for two -6an transmission lines.
This is a rough idea of how I wanted to run the lines. Along the frame rail, close to the wiring harness, where they can tuck behind the head shield (pulled up in this photo) and be 95% hidden and completely out of the way.
I mocked up the trans (not pictured) and measured where I needed to cut the lines under the tunnel, to have the proper length.
But how do you cut braided lines?
Not with cutters, lest you fray your stainless braid and try for hours to get the ends onto the cut hose. You use a large (3lb) sledgehammer or deadblow hammer and a chisel, or any large tool, and a chisel. I didn't have a large hammer handy, but I had a four pound brass pipe wrench, which functions just as well as a sledge, if not as sophisticated
Put the chisel where you want to cut the hose, and tap it a few times lightly, this will flatten the braid and hose. You have to use a hard surface that has no give. A metal block, vise, bench is preferred, but I don't have that in my garage. I used the concrete floor, works just as well.
This is the type of CLEAN cut a chisel and hammer gets you. Zero frays
An alternative method to cut the line is to wrap the end tightly with duct tape or electrical tape and cut it with a chop saw. This produces a similar no-fray end to the hammer+chisel method
Now that I cut the first line, I put the angle fitting on the transmission side of the line to fully assemble line #1. I then removed it from the car/trans cooler, and laid the remaining line next to it. The second line needs to be roughly 5-6 inches shorter then the first line, because it has roughly 5-6 inches less to travel (left vs right side output on the trans cooler). I laid the lines side by side, and trimmed the second line to 6 inches shorter, with the hammer/chisel.
The long line is 88 inches, the short line is 82 inches, not counting the fittings on the end. You can cut to these lengths beforehand to save yourself a lot of measuring, which I've done on my end already. Alternatively you could add a few inches to each line for some more flexibility with mounting if you so desired. This is simply what worked for me.
And just like that, you now have your burst and leak-proof transmission cooler lines. Doesnt this look better and sturdier then a shitty rubber hose, barb, and hose clamp?
I ran both lines into the engine bay through the lower radiator shroud pictured earlier. Here is what they look like with the heat shield reinstalled, completely out of the way. I also have the heater hoses behind the heat shield, for an extra clean engine bay.
The hoses come out just above the rear heat shield bolt.
And they go this far back into the tunnel, right in front of where the transmission cooler holes are, in an early 4L80e.
And finally, what it looks like behind the front bumper through the upper and lower grilles (finished)
If you have a late-core 4L80e, your line lengths will be different then mine. The early 4L80 cases have the cooler lines at the front of the case, instead of split like the later 4L80 cases. Since the early core cases fit better because of the cooler line locations, going with an early case is a no brainer.