What to do after building kernel on a VPS(Virtual Private Server)?
 

After successfully building the kernel on a VPS running Fedora, hosted on Digital Ocean, the book talks about configuring the host's grub file.

Since till now I have built the LFS on a VPS, how do I proceed from here?

To be precise the last command issued was
on this chapter.

Also, I have copied the kernel image, System.map and .config file to my local machine using scp.

"make install" should have copied the kernel to /boot. "update-grub" will find it and add it to your grub menu. Try it out before making it the default kernel.

There is no "make install" for LFS kernel in the book. You copy the 3 kernel files as the book says to /boot dir on your lfs build. You would rechroot per book and build the kernel right on the lfs vm not copy it using scp.

GRUB I assume you are goiing to use fedora grub to boot the new lfs so you want to read their docs on dual-booting linux and add the lfs to it's grub. Also make sure your fstab file is correct too. Finish with sect 9.3 rebooting.

Hope ya made the right choices in the kernel config for running on a VM vs real hardware.