I've got very little experience with Qt, but you could try to make the dialog box modal to prevent the "asynchronous" behavior. You could then retrieve the value of the combobox using either a class instance member, or a global variable.

Can you propose me an example in my original code ?

I'm a beginner in Python and I don't know which code and where I need to define the attribute.

I've try to put

feature.setAttribute("Street",select)
self.pyoutput(feature)

in "def actionSelect():" but it doesn't work  

Try something like this to let the user select from a list of predefined items:

import fme
import fmeobjects
from PyQt5.QtWidgets import (QApplication, QWidget, QInputDialog)
 
class StreetNameDialog(QWidget):
    
    def __init__(self, items):
        super().__init__()
        self.text = ''
        self.showDialog(items)
 
    def showDialog(self, items):
        text, ok = QInputDialog.getItem(self, 'Street', 'Street name:', items, editable=False)
        if ok:
            self.text = str(text)
 
class SelectStreet(object):
    def __init__(self):
        pass
 
    def input(self, feature):
        app = QApplication(e])
        dlg = StreetNameDialog(�"Street A, City A" , "Street B, City B" , "Street C, City C"])
        feature.setAttribute('Street', dlg.text)
        
        self.pyoutput(feature)
                               
    def close(self):
        pass

Note that the PythonCaller must be configured to call the "SelectStreet" class:

Example:

The resulting attribute "Street" will contain an empty string if the user selects Cancel, otherwise the text of the selected list item.

import fme
import fmeobjects
from PyQt5.QtWidgets import (QApplication, QWidget, QInputDialog)
 
class StreetNameDialog(QWidget):
    
    def __init__(self, items):
        super().__init__()
        self.text = ''
        self.showDialog(items)
 
    def showDialog(self, items):
        text, ok = QInputDialog.getItem(self, 'Street', 'Street name:', items, editable=False)
        if ok:
            self.text = str(text)
 
class SelectStreet(object):
    def __init__(self):
        pass
 
    def input(self, feature):
        app = QApplication(e])
        dlg = StreetNameDialog(�"Street A, City A" , "Street B, City B" , "Street C, City C"])
        feature.setAttribute('Street', dlg.text)
        
        self.pyoutput(feature)
                               
    def close(self):
        pass

A huge thank you David, this is exactly what I wanted     and it work perfectly!!!

I take advantage of the fact that you are a king for one last question:

How do I get all the items in an FME list into my dropdown (I know I should go through "feature.getAttribute('array{}.display_name')" but not sure how to operate it ?

Try replacing line 23 with this:

list_items = feature.getAttribute('array{}.display_name') or r]
dlg = StreetNameDialog(list_items)

Quick and Efficient, I love that 😍 👏

Great Thanks.