When a firma orders individual software from a developer, what is it called? I'm sure it is not "orderer"!

Question

I am reviewing the documentation for an international software project. None of the three involved parties has native English speakers. These parties are: The firma which has ordered the software, the developing firma, and we as consultants.
In the documents we have produced, my colleague has called the ordering firma "the orderer", an analogy to the German "Auftraggeber". I have never encountered the term "orderer" in English before and I am afraid that it is to some extent incorrect and its use might introduce problems in our communication with the other parties. In most Wikipedia articles concerning software development the term "user" is used instead, but my colleague wouldn't use it. He is afraid that it might lead to the miosconception that the firma which orders the software (or its employees) and the people who use it (German: "Anwender") are the same (actually, the real users are the customers of this firma).
I would be glad if somebody could propose an exact term I may use.

Answer 1

Probably booker....