There are several ways to do this, it just depends on what you are trying to do ... where are you trying to call PopulationComplete () in your ViewModel? For example, if you are in an instance of ICommand , you can pass it as a parameter, drop it, and call your method.
Based on your comment, I would approach this a little differently. This will be due to a number of workarounds due to control limitations.
Add an event listener to the view in the code behind, listening to the collection collection change event in your view model. Then you can call PopulateComplete () in the event handler. You will need a link to your ViewModel in your view for this.
Another option is to pass the link to the AutoComepleteBox to the ViewModel when the View loads (using EventTrigger) and stores the link in a private field. Then, when your web service call returns, use this link to call PopulateComplete ().
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