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Migrate a 32-bit debian installation to 64-bit one (i386 to x86_64)

After several attempts to find a solution which does not need a full reinstallation of the system I began to try the approach suits myself. I have to apologize right off because it is *UGLY*, but it has the benefit that you don't have to start an installation which might do something hazardous (e.g. repartition your system without even waving for your lost sensitive data). The principle is simple:

If you don't like the way, you are warned to stop reading me now! Or if you are not familiar with apt-get, dpkg and hacking small script, then this guide is not for you.

Check wether your Intel/AMD processor supports the 64-bit "long mode"

grep -q '^flags.* lm ' < /proc/cpuinfo && echo yes