How to Change Default File Manager?

Did removing the Nautilus File manager also remove integrated desktop environment elements?
Please double check that. The file manager governs the desktop, so the best practice is to leave the default file manager in place, and then install the new preferred file manager.

I recommend reinstalling Nautilus. Once installed and with pcmanfm still installed:
Open a terminal

sudo nano /etc/xdg/autostart/nautilus-autostart.desktop

Make sure the Exec line says Exec=nautilus --desktop then hit ctrl+x to exit, hit the y key to say yes to save, then hit the enter key to save configuration. The terminal will revert to normal. Now, enter:

sudo mv /usr/bin/nautilus /usr/bin/nautilus.bak

sudo ln -s /usr/bin/pcmanfm /usr/bin/nautilus