I'm ending the recruiting process in company A. Another company B is starting the process. I want Company B speeding up the process so I could choose the best fit offer to me.
Shuld I request recruiter of Company B to speed up the process because I'm in advance process in Company A ?
You may politely inform them when you receive an offer from Company A, and ask whether you're a contender for their position as well. If yes, maybe they can make up their minds right away whether to hire you or not.
Anything else is unreasonable, in my opinion.
Recruiters usually expect you to be engaged in processes with other companies. Some recruiters might even ask you about them, it happened to me quite a few times. You shouldn't ask Company B to speed up though. Just tell them you have an offer from Company A (if that's the case), and they will act in consequence : if they want you, they'll do what's needed. If you don't have an offer yet, then just tell them you've been in contact with A if they ask. But asking them to hurry will most likely make you look rude, impatient and/or presomptuous.
