"Favorites" Quick Saving Drop-Down

Trying to solve a problem where the client often has many similarly named items so even searching to filter can be difficult with only 1 or two letters different. The idea here was to allow "favoriting" items that then show first in the list for faster selection later on.

One question I am still unsure of though and debating:

Should the item be moved from it's original spot in the list once "favorited", and moved up to the top only? Or should it still be shown where it WAS in the list, as well as listed up top?