I hope you can feel a sense of peace in the coming days @Pushkinia .
We're all so different in the way we grieve, and the things that give us meaning. Funnily enough, I don't really connect my dad with his grave. I think I just see that as his earthly clothing. But, the real him, his soul, his energy, his animas, is live & well and free as a bird. I talk to him and the memory of him, loads, but oddly I don't think I would next time I visit the grave. I've only visited the grave once since the funeral, the day after the funeral, and did sort of talk to him there then, as it was such a new reality I'd nowhere near yet adjusted to.
Like you, I'm in a different country. My dad's buried in Ireland, and I live in England.
I definitely plan to visit it (the grave) and lay flowers next time I'm in Ireland, but I see it as a kind of memorial to him, rather than actually him, if that makes sense. I feel his presence more when I look at his old armchair, or in his garden etc.
But, I think if your mum's ashes are especially meaningful for you, then being far away must be really hard. I reckon those thoughts might lessen soon. But, in the meantime, hopefully the fact the grave will be well looked after is a comfort.
You take care, and be very kind to yourself. Lots of love x