… I suggest you download Picasa from the official website to have local access to the installer. While Google may keep it up after it shuts it down, you may want to have a backup of it at hand should you require one.
The download source was (on Filehippo.com): Picasa 3.9 B 141.259
This "Sunset" version was downloaded by me and saved as: picasa39-setup - v3.9 Build 141.259 (2015-10-14) Sunset version.exe
The file is apparently still available from there: Picasa 3.9 B 141.259
The download source at Filehippo.com (above) apparently no longer hosts that Picasa file.
However one can still obtain it from here, and it works just fine: picasa39-setup - v3.9 Build 141.259 (2015-10-14) Sunset version.exe