Question: I recently installed PostgreSQL 13 on windows 10 and the PostGIS extension via the stack builder. However, when trying to launch the shp2pgsql-gui application to import a shapefile, I get a "libsqlite3-0.dll was not found" error. I can see the file under the bin folder, so I'm not sure where the problem is and googling did not help very much. I wonder what the problem may be because the installation seemed pretty straightforward to have done something wrong.

Answer: 
Copying the "libsqlite3-0.dll" file from `\PostgreSQL\13\bin` to `PostgreSQL\13\bin\postgisgui` and then running the shp2pgsql-gui application seemed to fix this issue for me.
This problem can occur for different reasons, but I recommend that you download that .dll from the following link (<https://es.dll-files.com/libsqlite3-0.dll.html>). Then replace the file in the installation folder.