The lensless endoscope represents the ultimate limit in miniaturization of imaging tools: an image can be transmitted through a (multi-mode or multi-core) fiber by numerical or physical inversion of the fiber’s pre-measured transmission matrix. However, the transmission matrix changes completely with only minute conformational changes in the fiber, which has so far limited lensless endoscopes to fibers that must be kept static. In this paper, we report for the first time, to the best of our knowledge, a lensless endoscope that is exempt from the requirement of static fiber by designing and employing a custom-designed conformationally invariant fiber. We give experimental and theoretical validations and determine the parameter space over which the invariance is maintained.