I've read a lot of the forum but don't know exactly the phrases to search for

I have a live html website with good google ranking on the html pages.
I have just finished a duplicate site built with CMSMS, for the same domain.
I want to delete the old html pages, and just have the CMSMS website.
I realise I need to go into config.php and change the setting to extensions of '.html'.
My question is - do search engines keep the 'memory' of my html pages, and will my cmsms '.html' pages continue to have their rankings?
I am not sure how the whole CMS / php / database works in comparison to flat html pages.
Can anyone offer simple explanations for me? Pretty please?

Thanks in advance!