Reinstall GRUB for Arch Linux after Windows 10

This guide is for booting from UEFI.

Get an USB with Arch Linux ISO flash in (I use balena-etcher)
Boot from Arch (in UEFI mode)
$ fdisk -l to find out where the Arch installation partition and EFI partition are
Try mount, e.g., $ mount /dev/nvme0n1p1 /mnt to mount the Arch partition, "/dev/nvmeXn1pY" or "/dev/sdXY" (substitute "X" and "Y" with your disk/partition numbers), to /mnt
Try mount, e.g., $ mount /dev/nvme1n1p1 /boot/efi to mount the EFI partition, "/dev/nvmeXn1p1" or "/dev/sdX1" (substitute "X" with your partition number), to /boot/efi

Run $ mkdir /boot/efi, if there is no /boot/efi available, then mount again.
$ arch-chroot
$ grub-install --target=x86_64-efi --efi-directory=/boot/efi --bootloader=arch_linux
Reboot to test

Run the below, then reboot to test

$ sudo os-prober
$ grub-mkconfig -o /boot/grub/grub.cfg

If the entry is still not there, $ fdisk -l to look for YOUR EFI PARTITION, "/dev/nvmeXn1p1" or "/dev/sdX1" (substitute "X" with your partition number)
$ blkid /dev/nvme1n1p1 to get the UUID of the partition

$ nano /etc/grub.d/40_custom to manually add the entry (replace YOUR-UUID with the UUID got from step 3) at the end of the file

menuentry "Windows 10" --class windows --class os {
  serach --no-floppy --set=root --fs-uuid YOUR-UUID
  chainloader ($root)/EFI/Microsoft/Boot/bootmgdw.efi
}

$ grub-mkconfig -o /boot/grub/grub.cfg again, then reboot to test

Reinstall GRUB for Arch Linux after Windows 10

If the Entry of Windows Is not in GRUB Boot Menu

Refs