If the shasum is good, I don't know why it's not installing. However, there is a dirty hack you can use to install the files manually. You will need to extract the deb package and then copy the files to your system. Unfortunately, dpkg and apt will not know the package is installed so eventually, you will have to fix this problem or manually install future updates.
First, create a working directory and move the deb file into the directory:
mkdir apt-offline
mv apt-offline_1.8.2-1_all.deb ./apt-offline
cd apt-offline
Then, extract the files using the dpkg-deb command like this:
dpkg-deb -xv apt-offline_1.8.2-1_all.deb
Alternatively, if dpkg-deb is not installed (command not found), you can use ar and tar to extract the files instead:
ar xvf apt-offline_1.8.2-1_all.deb
tar xvf dat*
After you extract the files, use the following command to copy the files into your system:
sudo cp -R ./usr/* /usr/
To verify the installation, run the following command:
which apt-offline
and it should return: /usr/bin/apt-offline
Aside from the fact that you won't get automatic updates, the other problem is that you won't have bash completion.