Will the Amazon Fire TV stick remote control the Fire TV box?

Will the Amazon Fire TV stick remote control the Fire TV box?

I lost my remote, and was using the remote app. Then I changed internet providers, and now the box just comes up and says it has connection problems, and the app can't see it. A replacement remote takes 2 to 5 weeks and costs $30. The stock with remote also costs $30, but will arrive in 2 days. Will the stick's remote control my box so I can get it on my new network?

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