Is it possible to have tab autocompletion of remote files for SCP?

Question

Given host A / user a and host B / user b, and ssh from A to B: a@A$ ssh b@B. Suppose that in B there is a file called hello.txt. As we know, if I log into B and look for this file, I can use tab to autocomplete the file name:

a@A$ ssh b@B
b@B$ ls h
  hello.txt

where at the end of the second line I typed 'tab'.

Now suppose that I am logged into A and I want to copy with scp hello.txt from B to A, but I do not remember the full file name, I only remember that the file starts with 'h'. I would like to do

a@A$ scp b@B:h

then press 'tab', and see the list of files in B that start with 'h', just like in the example above. Is this possible?

Edit:

Here is how I tried to do this by following pLumo's suggested answer:

    $ ssh b@B
    Last login: xxx
    b@B:~$ ls
    my_file.dat
    b@B:~$ exit
    logout
    Shared connection to B closed.
    $ cat ~/.ssh/config
      Host B

          Hostname B.xxxx.xx

          User b


          ControlMaster auto    
           ControlPath ~/.ssh/control:%h:%p:%r

    $ scp b@B:my_file.dat .
    my_file.dat                                                                                                                                   100%    4     0.0KB/s   00:00  
    $ssh -fN b@B  
    $ scp b@B:my_ 

where at the end of the last line I pressed TAB, but nothing happens. 

Answer 1

Tab completion works well for scp if you have one of these:

---

First option:

Reuse connections, add this to your ~/.ssh/config:

Host B
    User b
    ControlMaster auto
    ControlPath ~/.ssh/control:%h:%p:%r

For tab completion to work, you need to have a connection already open. You can start one in the background if you don't have one already open:

ssh -fN B

This even works via JumpHost.

---

Second option:

Use Public/Pricate Keys, scp will automatically use these. Downside is, scp will need to login each time which might be a bit slower than reusing already established connections.