I can hopefully give you another way of thinking about this situation.

 Low back pain may have different basis.

#1 Imbalance stomach to back musculature.

#2 Kidney function 

#3 Infection ( intestinal and spinal tissue )

#4 Disc problem

#5 Chronic muscle overuse in any of the back muscles

#6 Transposition of muscle loading ( due to amputation )

As to #6 I would suggest that people are of 3 types when standing.

A.  Stand with locked knee - muscle tension on Calves and Hamstrings

B.  Stand with unlocked knee - muscle tension on Quads.

C.  Distributed muscle contraction - a neutral stance.

Muscle overuse and injury can cause chronic activation of muscle spindle cells and 24/7 hyper tonus.  Therapeutic massage can help address this.  A top level sports massage expert should assess possible treatment.  Cold treatment is NOT recommended by my experience, - and is of dwindling value according to recent investigations.

Stance in the case of Type A. Or type C.  - may signal the opposing muscle group to relax, - chronic relaxation can decondition that relaxed group - due to muscle overuse in the contracted muscle.  Amputation would likely acerbate any existing status - altering patterns of chronic overload.  

Careful examination requires an enlightened approach to thinking through a list - such as this, but of course including any additional factors which can be helpful.

Hi Bastien, Have you considered the use of Inspiratory muscle training for this? There is evidence emerging that strengthening the diaphragm which is one of only a few muscles to insert directly onto the lumbar spine helps reduce lower back pain. This occurs by increasing the strength / cross sectional area of the diaphragm and naturally its origins/insertions  will therefore increase. This has a positive effect on increasing spinal stiffness and is becoming a common non-pharmocological treatmetn for lower back pain. There is some convincing evidence surrounding this and its affects on attenuating lower back pain by increasing postural stability and postural control in healthy able bodied groups by Lotte Jannsens and Alison McConnell that I'd be happy to send across to you. 

Basic physiotherapeutic interventions are still beneficial in managing lower back pain especially in resource limited areas. But assessment should form the basis of your management programmes.

JUST REMEMBER THAT POST TRAUMATIC SYNDROME AND POST AMPUTATION SYNDROME ARE DIFFICULT TO TREAT BUT NOT IMPOSSIBLE! Bon Chance

Bastian,

all of the above is helpful especially the trauma comment.  The resolution not management of the condition lies in an understanding of episodic memory as it relates to a hyper awareness neuroendocrine and neuromotor response to what should be normal sensory data.  Another way to consider the problem is that a normal reflexive response like a crossed extensor reflex that is not reregulated secondary to the brain still requires it to be a low level because the trauma was significant enough to have long term potentiation circuitry develop.  This may be one of the reasons why some breathing techniques have shown promise in inhibiting the reflex. I personally use Associative Awareness Technique it's a relatively new treatment regimen worth a look if nothing else. A good resource can be found at truamasoma.com Dr. Robert Scaer there are articles there that describe the basics of understanding the problem.  A great article that lays out the foundation of trauma processing in an evidence based manner is by M. Liang, A. Mouraux, and G. D. Ianetti, Bypassing Primary Sensory Cortices-A Direct Thamlamocortical Pathway for Transmitting Salient Sensory Information.  The article lays out very well circuitry that is responsible for survival based behavioral response that has run amok. 

Unfortunately, there are no standardized programs, ottobock has an app but it's not focused specifically on lbp. There are a few made by amputees themselves. I have a project on this, let me know if you are interested to chat

There are several areas in cases of low back pain in above knee amputees using prostheses that should be carefully evaluated regarding the prosthesis:

1.proper fit of the socket in mid-stance and proper suspension in swing phase

2.proper flexion angle of the socket(anatomical flexion plus 5 degrees) at mid-stance

3.adequate anterior placement of the correctly flexed socket relative to the knee center at full extension of the knee and foot flat

4.vertical pylon with even contact of the foot in the shoe and the shoe with the floor in mid-stance

5.correct overall length of the prosthesis to facilitate ambulation, approximately 1/2" shorter than sound side except in bilateral cases which should be even