How do i seperate a transmission from a 06 lincoln ls 3.9 engine

Fuse box diagram.
https://www.autogenius.info/lincoln-ls-2000-2006-fuse-box-diagram/
Some good info on fan operation of you car on below link.
https://www.justanswer.com/ford-lincoln/7k3bc-lincoln-ls-05-lincoln-ls-cooling-fans.html

Just a thought: If you have two electric fans one comes on when you turn the A/C on the other does not come on till the car reaches normal operating engine coolant water temperature.

tire seperation,,bent wheel,tire out of balance,,,very loose tie rod ends,,prob. a tire trying to seperate,,,b careful

It's old question, you might find it out already.
If not, here is pictures and diagrams.
It might be two different routing.
Mine is limo which has two alternators.
try to see which is yours.
(red was mine with two alternators. original is black in diagram)

also you may know how to loosen serpentine by insert and turn 3/8 drive ratchet (just ratchet without any socket) to tensioner pulley if not, here is picture (I use 3/8 ratchet + pipe).
Picture was taken after 2nd alternator removed (around upper hose)

Whether is a 3.0 or 3.9 engine there is no C solenoid, The transmission is a 5R55N it has no C solenoid.

Hello, It engine is pulled out from the tope, Remove the hood, remove the radiator, move ac dry and condinser to the side and disconnect the transmission cooler linges, disconnect the auto transmission from the engine, remove the starter, remove the exhaust flanges at the exhaust headers. Also, the engine is a V-8 4.6 litre. GB..stewbison

You replace the Transmission Pressure Control Solenoid Pack

There are 3 pressure control solenoids & 4 shift solenoids in one
plastic part ,made by Bosch

You remove the trans pan,the gasket is reuseable silicone
You remove the filter
You remove approx 7 -- T30 bolts, holding the solenoid pack
& one 10mm electrical connector bolt

HPN-9L2Z7G391A $515.30 / $ 332.20 cost -- for part

usually shift kit makes for harder shift also verify engine is well tuned.

on the right side of the engine compartment you should find a red plastic dipstick remove it from tube and check fluid mark do this on level ground and engine idling in park. fluid has to be between the add and full marks at bottom of stick use dexron 3 automatic transmission fluid the fluid is added into the tube the stick came out of.

The engine should be separated from the trans at least 1 "and the torqu convert slid into the trans. There may be a dowel pin on each side. That is wh the one inc.

Did you disconnect the torque converter bolts also? If so, get a jack, support the tranny and pull motor from the trans.