On iPhone:
When she sends them press the three dots in the top right and save to chat (I do this and she hasn't complained). You can do this to her story posts as well. Put your phone in airplane mode then tap and hold the pic/video in your chat with her and choose save to camera roll. You can do this for multiple items at once as long as you loaded them up before going airplane mode, maybe 10 or 20. Once you're done saving them, uninstall snapchat from your phone before turning off airplane mode. No notification will be sent as long as you delete the app before reconnecting to the internet. You can download Snapchat again right away, it won't remember that you saved items to the camera roll and no notification will be sent. It should remember your login though and open your account easily without hassle, so this whole process can be pretty quick and easy.
This has worked for me for years but I usually test it against an alt snapchat account to be sure if I haven't done it for a while.
On Android I can't promise this will work because they're all very different.