Objects that get destroyed when they lose focus can be tricky.
My normal approach is to get what I can with CTRL + SHIFT + A. Which will at least give you a snapshot of the object at that point. From there, I tend to take the parent object (which is a property of the capture you have) and then write a little routine to trigger the transient object. Then using break points, gathered properties, and anything else I can get from debug info once paused.
But it very much depends how helpful, or not, the object is. In the few cases I've had to resort to this, I've managed to find what I need to manipulate them to do what I need.
I don't map objects like this. Just use routines to handle them dynamically at runtime.
Other possibilities are ....
1. If the object is a certain class/type of control, look up the documentation for it! You can usually get a lot of info on what *should* be available using this.
2. If they are available, speak to the dev team. They wrote it, so they should know what it is, how to control it, and how it behaves.
The dropdown should be similar to the tool strip. The options are not objects. They are part of the dropdown. So you'd map the dropdown and use a method to search/find/change the current option. Exactly how depends on the dropdown. There are loads of different types and how you manipulate them varies. Or, of course, it could be an entirely custom control the dev guys have built. It happens.