Can you disclose your stuttering to them before moving? I’ve found a lot of tension realized as soon as I go into difficult situations where I expect to stutter like interviews or meeting new people. If your stuttering is severe and they know it then they’ll have realistic expectations and maybe they could give you some accommodations (like communication via text and email instead of verbal). The fact that you have been working for them 6 months and they offer you a job over there means that you’ve been doing your work well regardless of your stuttering and you can still do so when moving.