Private Deploy of EF with SQL CE 4.0 and Click Once

Recently I faced the problem with deploying an WPF application, which uses Entity Framework and Sql Server Compact 4.0 nuget packages. The application was deployed automatically by TFS Server as a Click Once  installer. The problem was that the setup did not download Sql Server package at client machine and application could not work. Apart from checking what is maybe wrong on TFS side configuration, the simplest solution was to do a so called Private Deploy of the Sql CE libraries. Unfortunately it turned out to not be easy too.