The only way I know of to make that work would be to connect the original/old phone, with the SD card in it, to a computer via USB cord. Then create a folder for the files on the computer and move whatever it is you want to keep from both the phone itself (other than apps) and the SD card over to the folder on the computer.
Then disconnect that phone from the computer and connect the new phone, with the new SD card already in the new phone, via USB cord to the same computer. All you need to do then is copy the files from the folder on the computer over to the new phones SD card.
It is always smarter to make the changes this way, when the card is still in its device, rather than pulling a card and trying to move data that way.