[This response should not be construed as a Halachic ruling on the question. Rather, it is an exploration of the topic to help our readers become more familiar with the issues involved.]

There is quite a discussion among the Rishonim and Acharonim whether this is an option, or the woman should pay for the Get. The Aruch Hashulchan (E.H. 120:17) says that this is an option, but notes that the Beis Yosef and Gra (ibid.) understand that the Rambam holds that it should be done this way (unlike the Rosh and Tur, who clearly states this is an option). I am unsure how each Beis Din applies the Halachah.

[I hope this response has clarified the issue. For all practical questions on the issue, please consult your local Orthodox rabbi.]

All the best,

Yaakov Montrose