Hello All,
Looking for some help here on my TCM P56044737AI is working Intermittently, I was looking for a TCM replacement but I just find out that there are 2 that works with my Liberty CRD 06.

What is the difference between TCM P56044737AI and P56044737AF?

Most likely the same part. P56044737AI is just a later version or revision of the same part number P56044737AF.
Mopar normally just changes the last letter of the part number as they update or modify the part.

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Supporting Vendor and Moderator of LOST
05 Jeep Liberty CRD Limited
Ironman Springs/Bilstein/Shocks
Yeti StgIV Hot Tune
Week's BatteryTray
No FCV/EGR
Samcos/ProVent
SunCoast/Transgo
Carter Intank-pmp
2mic.Sec.Fuel Filter
Flowmaster/NO CAT
V6Airbox/noVH
GM11 Bld.fan/HDClutch
IronrockArms/wwdieselMount
98 Dodge Cummins 24 Valve

Yes the last two characters are just a revision number.

AI will be a slightly newer revision than the AF but there should no noticeable differences.

What is wrong with your existing ECM?

The ECM tends to be a pretty reliable unit...most problems are wiring related!

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2002 Export CRD

I recommend removing inspecting and cleaning the contacts and make sure all groups are good first then look for frayed wiring etc if that doesn't help unless you have knowledge of another reason for the malfunction.

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05 Blu LIM, OME GDE Tbo, wk II 245/75/17, KC Lights, bull bar, 195K H TC
05 Blu Lim, Dayton, GDE HT, 255/75/18 , 210K , H TC
06 Bla Lim, GDE Eco, Destination AT 245/75/17, 151K, H TC
06 D Khaki Lim 126K wkII Eur TC
05 D khaki Lim 145k refurbishing
All CRDS: Fumoto, Lift , Fan Shroud mod, fuel head Gen II, SAMCOS,self TB, 2 Mic filt, Hayden

I put deoxit on the connectors whenever my TCM throws a code.

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2006 LTD Bright Silver loaded with all the needed mods, CCV intact.
Proudly supporting CRD vendors, and their development of quality parts and accessories.
Equipped with HDS thermostat, plenty of heat, faster warm-ups, increased fuel mileage.