Is it permissible for a trainer to use pirated software in his work, and does he bear sin if he trains engineers who will use it pirated for profit, knowing its impermissibility?

The salary a teacher receives for the courses they provide is permissible (halal), because it is paid for their effort and work, not for the pirated software they might use.

However, the teacher is accountable for using pirated software, and the owners of these programs have a financial right against them, estimated by the loss of benefits from their programs and the damages incurred by them.

As for training engineers, there is no objection to it. The burden of using pirated software falls upon them, and it is sufficient for the teacher to explain to them the impermissibility of infringing on intellectual property rights.