This is a phenomenon that refers to the sensation of having non-human body parts attached to the human body. Phantom shifts are most commonly reported as being wings, tails, muzzles, scales, claws, and fur.  While the vast majority of therians experience phantom limbs, a minority do not.
- See also: Therianthropic Shifts
Some therians have noted that they have felt pain, itching or discomfort during phantom shifts. A number of therians state that they do not have phantom shifts, per se, but instead always feel their phantom limbs.
"The specific ways in which these can be experienced varies vastly, but included amongst them are a diversity of levels of ‘realism’, some being very minor to some even being so intense that the phantom part feels almost entirely “real” regardless of the fact it is not physical. Some phantom parts are constant, but the ones referred to in this definition are those that are temporary and ‘shift’ in and out of occurrence. Other effects associated with some phantom parts include pain or discomfort in/on or associated with the phantom part, movement (voluntary or involuntary) of the phantom body part, and reactions to outside ‘real’ stimuli such as objects, sounds, movement of other things, and so forth." - Project Shift 
Related Reading and Art
"Regarding Phantom Limbs" by Orion Scribner (2015) - http://frameacloud.tumblr.com/post/125287555871/regarding-phantom-limbs
Theri There Comic "Introduction to Phantom Limbs" by Orion Scribner (2005) - https://tapas.io/episode/291750
Rubber Hand Illusion
One does not need to be Therian or an amputee to experience phantom limbs. Experiments prove that people can be fooled into thinking that another object or even an invisible limb is part of them. The deception is known as the rubber hand illusion.  
- ↑ Shifters.org Encyclopedia - http://web.archive.org/web/20060821231409/http://www.therianthropy.org/SO/terms-p.htm
- ↑ "Types of Shifts" written by Sonne, hosted on Project Shift - http://project-shift.net/types-of-shifts/
- ↑ "Phantom Extra Limbs" Mind Hacks, May 14, 2008, https://mindhacks.com/2008/05/14/phantom-extra-limbs/
- ↑ Choi, Charles Q. “Even Non-Amputee Can Feel A Phantom Limb,” Live Science, April 12 2013, http://www.livescience.com/28694-non-amputees-feel-phantom-limb.html (accessed June 25 2016)