The best replacement for mailbox is distribution list.

The best alternatives to mailbox are rated as following:
★★★★★  distribution list
★★★★★  boxer
★★★★  smart mailbox
★★★★  mailbox
★★★★  gmail
★★★  mail pilot
★★★  gmail app
★★★  maildir
★★★  mail box
★★★  mail
★★  po box
★★  ios 7 mail
★★  distribution group
★★  letterbox
★★  sanebox
★★  airmail
★  mail contact
★  sparrow
★  smart mailbox folder
★  user mailbox
★  public folder
★  usps po box
★  dispatch
  cloudmagic
  inbox
  evomail
  mail slot
  boomerang

Your alternative for mailbox is not listed? Suggest!
Speaking about mailbox, one probably shouldn't forget about user account.

Other search terms related to mailbox and their ratings are:
★★★★★ user account
★★ ad account
★ deleting user
You have in mind a companion for mailbox and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of mailbox in all years. Click on graph for more.
mailbox
distribution list
boxer