@M.Gimenez You could just install the libs with your package. It may be against the stdc++ license but putting the version you expect on the target device will make it work.
Speaking of licensing, know that static building with Qt requires a commercial license and is not available for the open source license.
So to explain this a bit more, when I package my linux apps, they look something like this:
fonts/
*.ttf
bin/
myapp
libs/
libgcc_s.so.1
libQt5Core.so.5
libQt5Gui.so.5
libQt5Network.so.5
libQt5Widgets.so.5
libstdc++.so.6
resources/
image.png
myapp
README
myapp in the root package dir is a start script like so:
#!/bin/sh
dir="$(dirname `readlink -f $0`)"
LD_LIBRARY_PATH="$dir/libs:$LD_LIBRARY_PATH"
QT_QPA_FONTDIR="$dir/fonts"
export LD_LIBRARY_PATH QT_QPA_FONTDIR
exec $dir/bin/myapp "$\@"
Again, please keep in mind you need to follow licensing. The above app was developed with Qt Commercial licensing. Even though I didn't use static linking it was a commercial app so I could have used it but preferred dynamic linking.
Hope that helps in some way. :)