Q:

How to connect two QLineEdit to have the same inputs (controlled by a QCheckBox)

I have two line-edits (le_A and le_B) that only take numeric values and a check-box (chk_box). I am having issues in getting le_A and le_B to have the same inputs (see Scenario 2 below) whenever chk_box is checked (where chk_box is the 'controller').
Example scenarios:

Scenario 1. User can input in any value in le_A or le_B when it is unchecked. For example, value in le_A is 10, while le_B is 20. 
Scenario 2. Any values that User input in le_A and le_B will be the same when it is checked. For example, if I input 10 into le_A, le_B will be 10. And the same goes for input done in le_B - the same value will be shown in le_A.   

Code:
class CustomTest(QtGui.QWidget):
    def __init__(self, parent=None):
        super(CustomTest, self).__init__(parent)

        # Only numeric values
        self.le_A = QtGui.QLineEdit()        
        self.le_B = QtGui.QLineEdit()

        self.chk_box = QtGui.QCheckBox()

        lyt = QtGui.QHBoxLayout()
        lyt.addWidget(self.le_A)
        lyt.addWidget(self.le_B)
        lyt.addWidget(self.chk_box)

        self.setLayout(lyt)

        self.set_connections()

    def set_connections(self):
        self.chk_box.stateChanged.connect(self.chk_toggle)

    def chk_toggle(self):
        chk_value = self.chk_box.isChecked()
        a_val = self.le_A.text()
        b_val = self.le_B.text()

        # Inputs in either le_A and le_B should be the same
        if chk_value:
            # If the values are different, always use a_val as the base value
            if a_val != b_val:
                self.le_B.setText(str(b_val))
        else:
            # Inputs in either le_A and le_B can be different
            # Currently this is working
            pass

    if __name__ == "__main__":
        app = QtGui.QApplication(sys.argv)
        w = CustomTest()
        w.show()
        sys.exit(app.exec_())

A:

So if I understand your requirements correctly, when the checkbox is checked, you want to synchronise the text of the  line-edits - and then also keep them the same whenever the user enters any new text. If so, the following changes will achieve that:
class CustomTest(QtGui.QWidget):
    ...
    def set_connections(self):
        self.chk_box.stateChanged.connect(self.change_text)
        self.le_A.textChanged.connect(self.change_text)
        self.le_B.textChanged.connect(self.change_text)

    def change_text(self, text):
        if self.chk_box.isChecked():
            sender = self.sender()
            if sender is self.chk_box:
                self.le_B.setText(self.le_A.text())
            elif sender is self.le_A:
                self.le_B.setText(text)
            else:
                self.le_A.setText(text)

