Wx.stc.StyledTextCtrl ScrollBar

In my project, I use wx.stc.StyledTextCtrl(). I bind the events of key down and key up. When I want to add a letter into the TextCtrl, I don’t skip the event, in some reasons, I use the method AddText() in order to add a text. When the text is long and the ScrollBar (of the width of the screen) is opened I want that ScrollBar will be at the position where I can see the letter that is added (will move automatically as it should be). currently the ScrollBar always stays at the left side of the screen. I'm searching for a function that can do that.

when the letters are over the width of the TextCtrl (over pos 300) the ScrollBar is still doesn't move. I want that it will be like the messageTxt in the right side of the frame. Here is a basic code that present my problem:

import wx
import wx.stc

def on_key_down(event):
    pass
def on_key_up(event):
    key_code = event.GetKeyCode()
    messageTxt.AddText(chr(key_code))

app = wx.App()
frame = wx.Frame(None, -1, title='2', pos=(0, 0), size=(500, 500))
frame.Show(True)
messageTxt = wx.stc.StyledTextCtrl(frame, id=wx.ID_ANY, pos=(0, 0), size=(300, 300),
                                     style=wx.TE_MULTILINE, name="File")
messageTxt.Bind(wx.EVT_KEY_DOWN, on_key_down)
messageTxt.Bind(wx.EVT_KEY_UP, on_key_up)
messageTxt2 = wx.stc.StyledTextCtrl(frame, id=wx.ID_ANY, pos=(320, 0), size=(150, 150),
                                   style=wx.TE_MULTILINE, name="File")

app.SetTopWindow(frame)
app.MainLoop()

I've added a different answer because the first issue is still valid, just not for your question, as I interpret it.
I assume this is a mock-up of your problem, if it isn't, let me know and I'll delete it.
The "server updates" are simulated by a timer, the character is added, then we simply move the cursor 1 character to the right.

import wx
import wx.stc

server_sends=['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','T','a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','T']

class MyFrame(wx.Frame):
    def __init__(self, parent, id=wx.ID_ANY, title=""):
        super(MyFrame, self).__init__(parent, id, title)
        self.SetSize((500,500))
        self.panel = wx.Panel(self, -1 , size=(500,500))
        self.messageTxt = wx.stc.StyledTextCtrl(self.panel, id=wx.ID_ANY, pos=(0, 0), size=(300, 300),
                                     style=wx.TE_MULTILINE, name="File")
        self.messageTxt2 = wx.stc.StyledTextCtrl(self.panel, id=wx.ID_ANY, pos=(320, 0), size=(150, 150),                                   style=wx.TE_MULTILINE, name="File")
        self.timer = wx.Timer(self)
        self.Bind(wx.EVT_TIMER, self.OnTimer, self.timer)
        self.timer.Start(500)
        self.cnt = 0
        self.Show()

    def OnTimer(self, event):
        print (server_sends[self.cnt])
        self.Server_Update(server_sends[self.cnt])
        self.cnt += 1
        if self.cnt > len(server_sends) - 1 :
            self.timer.Stop()

    def Server_Update(self,char):
        self.messageTxt.AddText(char)
        self.messageTxt.CharRight()

if __name__ == "__main__":
    app = wx.App()
    frame = MyFrame(None,title="The Main Frame")
    app.MainLoop()