The answer to the problem is well known( http://www.math.uni-kiel.de/geometrie/klein/math/geometry/moufang.html ) that ; since :
all the PTRs coordinatizing a given projective plane are isomorphic iff it is a moufang plane iff all these PTRS are isomorphic alternative division rings.
The answer to the problem is well known. http://www.math.uni-kiel.de/geometrie/klein/math/geometry/moufang.html
However the problem to give a purely algebraic proof of this result seem to be an open problem.