Essentially, when one moves a keyword within an account to a different ad group, it does keep a lot of the keyword quality.
However, a keyword in a new adgroup is treated as a new keyword for part of the algo. This is due to it being in a new adgroup, possibly a different campaign (and thus different settings), different ad copy, etc. So, while part of the keyword QS is utilized, the QS is not transfered in its entirety. It also builds up CTR (a major part of the QS formula) within the new ad group, and this can also play a part on how successful a keyword is moved.
Overall, I've seen keywords pick up speed pretty quickly after being moved. However, in some very competitive industries, I've seen the keyword need to be forced through with a bit higher bid to get that traction as well.
Hence, I always recommend moving the lower preforming keywords and not the preforming ones for 'just in case' scenarios.