Your question is somewhat ambiguous. Do you mean you are "transitioning objects from S3 standard class to S3 glacier class", or are you copying them from S3 to the standalone Glacier service? Glacier standalone IMHO is somewhat legacy and doesn't seem to get updates. You also mentioned "copy files" - you don't typically copy files to change their storage class, you transition their storage class. Can you please edit your question to be more precise.
To answer your last question though, yes you can transition an object from S3 standard to S3 glacier class using the GUI. You click the object, select the properties tab, then click storage storage class, the click the current storage class. That gives you the option to change it. There will be an API call, but I don't know what it is without researching it. Google will find it if you search for something like "AWS S3 API change object storage class".