Hello!
I can see this is a recurring issue. I was just searching for the same feature today, as my Import from an another e-mail provider created a second “Sent” folder and I want to merge them. Actually, it’s the same usecase as here.
When selecting all e-mail in the folder, I can drag & drop them to Runbox’s Sent folder, but it only moves the e-mails shown on screen (~25 to 30 maximum, when the whole folder content is selected and counts 2500+ e-mails).
My workaround will be to use Thunderbird, but it would definitely be nice to see this feature actived (if it does not imply a huge work of course): if moving e-mails to Sent folder is not common as a daily task, IMO it gets common when coming to migration processes from another hosting service.
Of course, this is just an opinion 
Have a nice day,
K.