Hi Dears,

Is it possible that if an employer says to arbeitsamt that my employee has been finding out jobs and applying jobs to other firms or they have proof that he has been trying to find out jobs to other firms.Is it also unofficial or unlawfull or problem in green card law???

It's not forbidden to apply for a new job while employed in a different job. Actually this is the recommended way to change jobs, with no intermediate unemployment.

However during working hours employees are expected to spend their time working and not making private arrangements, even though in most environments a certain amount of private activity is tolerated, such as taking or making the odd phone-call.