This code demonstrates features that are not well documented at this time. The main feature is that the selected mailbox in imap_open (or reopen)  and the specified mailbox in other imap functions are unrelated.  It has been tested with Gmail and with a Dovecot IMAP server.  The mailbox separator depends on the server. Gmail: "/"  Dovecot: "."  If you want to test with Gmail, you need to turn on "Access for less secure apps" in your account.
 
<?php
  // Change these.
  $server    = "{imap.gmail.com:993/imap/ssl/novalidate-cert}"; 
  $email     = "example@gmail.com"; 
  $password  = "password";
 
  // The code assumes that the folders Test/Sub1/Sub11, etc. exist. 
  $selected  = "{$server}Test/Sub1/Sub12";
  $conn      = imap_open($selected, $email , $password);

  // This returns the $specified mailbox and its sub mailboxes, 
  // even if the $specified mailbox is outside the $selected mailbox. 
  $specified =  "{$server}Test/Sub1"; 
  $boxes     = imap_list($conn, $specified , '*');
  print_r($boxes);
  
  // This appends the message in the $specified mailbox. 
  // It ignores the $selected mailbox. 
  imap_append($conn, $specified
                     , "From: me@example.com\r\n"
                     . "To: you@example.com\r\n"
                     . "Subject: test\r\n"
                     . "\r\n"
                     . "this is a test message, please ignore\r\n");

  // This changes the $selected mailbox
  $selected = "{$server}Test/Sub1"; 
  imap_reopen($conn, $selected); 

  // This moves a message from the $selected to the $specified mailbox
  // In this case, the specified mailbox does not include the server. 
  imap_mail_move ($conn , "1" ,  "Test"); 
  imap_expunge($conn); 
  imap_close($conn);
  // If you executed this code with a real IMAP server, 
  // the message is now in the Test mailbox !
?>