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I have completed two job interviews.
One company emailed me 2 weeks ago telling that I'm shortlisted for hiring, and even the manager sent me a message personally, whether I have received an offer letter and asked me to wait for HR to do a background check (since I mention I haven't heard any update from HR). Should I follow up on HR again since the last time that I email them is after HR said that I'm shortlisted for hiring (before manager sent me the message) or should I wait for 1 week more? Another one asked me to email my document since he didn't take my hard copy even though in job invitation clearly ask me to bring those. It has been 5 days since the interview happens (including weekends). Should I email the document now and ask for follow up (I really like the job and the manager)? Is it okay for a candidate to keep bother the hiring company?