What is the ruling on a female student participating in an invention idea with a school owned by the church, knowing that the school will bear the costs of the patent and then share the profits with the student?

It is permissible for a Muslim to strive to obtain a patent if the idea is beneficial in permissible matters, and there is no harm in a Christian school participating in acquiring it and sharing its proceeds. For, it is permissible to partner with a disbeliever and trade with him, except for selling weapons to a belligerent disbeliever. Al-Bukhari narrated from Abd al-Rahman ibn Abi Bakr that the Prophet, peace and blessings be upon him, bought a sheep from a polytheist. Muslims have unanimously agreed on the permissibility of dealing with Dhimmis and other disbelievers, provided that what is involved is not forbidden. However, it is not permissible for a Muslim to sell weapons, war instruments, or anything that helps them establish their religion to people of war. Similarly, there is no objection to accepting assistance from the church in this matter, as long as it does not lead to renouncing one's religion or involve humiliation and degradation for the Muslim.