Hi,
my thanks again for proposed simple solution. I realized better that it is useful after I had read the documentation, Simulating Keystrokes | TestComplete Documentation (smartbear.com):
"Note that the SetText action changes the object text programmatically, so, it may take less time to execute. The Keys, KeyDown and KeyUp methods, in their turn, simulate actual key presses in the object, taking into account the Key pressing delay project setting. However, the key pressing methods also ensure that the appropriate keyboard events are raised in the tested application and the associated event handlers, if any, are executed. Therefore, these methods are preferable to SetText in certain cases."
As the result, we have decided to replace the usage of .wText := ... and .setText(...) by the calls of Keys(...) method everywhere it is allowed by the control. The remaining cases are those where the controls have a derived java class that does not support the Keys() method and so it is required to call .setText(). For these cases the initial issue is actual as the calls may be executed in the context of automation thread and lead to possible failure. We sent the request to support and now are waiting for the results of analysis.