What is the ruling on work that requires shortening the beard and missing the 'Asr prayer in the mosque, or working on developing computer programs to facilitate stock trading for foreign companies, given the opportunity for emigration after two years of working in the field?

If the intended meaning of trimming the beard is to remove what is unruly and straggly, or what exceeds a fistful, then there is no objection to that, as well as removing hair growing on the neck, throat, or below the eyes. There is also no objection to performing congregational prayer at work for a legitimate reason. Therefore, there is no objection to accepting this job.

However, if trimming implies severe shortening of the beard, or abandoning congregational prayer in the mosque without a legitimate reason, then it is not permissible to accept this job unless there is a compelling necessity.

Working in this latter case (necessity) takes precedence, according to Islamic law, over other work that involves assisting in unlawful dealings, such as usury and other forbidden acts. Any job that does not necessitate engaging in something forbidden, abandoning an obligation, or assisting in such, is permissible; otherwise, it is forbidden.