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If you don't want to install 7zip, you can monitor your local TEMP dir, such as c:\windows\users\<user>\AppData\Local\Temp\ and look for a just created 7z.....tmp dir just after you have started the installation and the files are extracted.
This dir. you can copy and save with another name , if a reinstallation of basecamp is needed. Just start the BCMAIN.msi.