Can a teacher skip parts of davening if he is running late in the morning? In this teshuva, Rav Moshe Feinstein says that in such a case, the teacher can most definitely skip פסוקי דזמרא. He offers two rationales for this. First, if he were to come late to class he would be taking away learning time from his students; second, coming late to class would constitute stealing from his employer, who is paying him to be at work at a certain time. Rav Moshe notes that if the issue is that the teacher has his own work to do he should not skip any part of davening.
Rav Moshe does note the option of saying הביננו, which is a severely shortened version of שמונה עשרה, but concludes that since it is so rarely, if ever, said these days it is unlikely that the teacher will know it and thus the time saving as a result is likely to be minimal.