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does she like a certain animal or video game character that you could draw? (even badly the effort is the most that counts)
well from your other comment im sure she would love a drawing of any sort. :D
so true who doesnt like having a shiny conversation starter about ur love
If she has a favourite moment/picture/drawing then it would be really sweet if you come somehow send it to her as a postcard, with a letter to her on the back (best wishes, memory recollection, season's greetings, wishes for the future... anything you wanna write about) and have it so it arrives on Christmas Eve :)
Hmm... online could work. Have you seen those shows where they find old USBs or CDs or folders with a video message in them? You could do that same kinda thing. Maybe send her a DO_NOT_OPEN_TIL_XMAS.zip or something, with a recording of yourself talking to her in it, saying the same kinda thing. The upsides to this are a) she gets to see you and b) it can't get lost in the mail. It is a bit less personal and definitely less tangible, but it can work.
could you order a personalized gift delivered from in the country? ex like the same meal but hers is from a resturant near her and yours is from a resturant near you
edit: see no address so idrc if you havent been physical before no stress about a physical present now