引入偏序半群的商半拟序的概念，利用商半拟序给出了可消偏序半群上的偏序可扩张为可消偏序的充分条件.通过偏序半群的半拟序σ、模σ的闭半拟链，商半拟序和偏序扩张以及可消偏序半群的可消偏序扩张，对偏序半群的商序同态进行了刻画，得到了若干重要的结论.Abstract：This paper studies the cancellative partial ordered extension and properties of quotient ordered homomorphisms of cancellative partially ordered semigroups(CPOS). The notion on quotient semi-pseudoorder of partially ordered semigroup(POS) is introduced. With the quotient semi-pseudoorder of CPOS and using the method of partial ordered extension of POS, the sufficient condition for extending a cancellative partial order of CPOS to another cancellative partial order is derived. It is also shown that quotient ordered homomorphism of partially ordered semigroup POS can be depicted by semi-pseudoorder σ, closed semi-pseudochain of modulo σ, quotient semi-pseudoorder, partial ordered extension of partially ordered semigroup, and cancellative partial ordered extension of CPOS. Some important conclusions are obtained.