Hi, @yanou
The chat bubble div is:
<div class=”fb_dialog fb_dialog_advanced fb_customer_chat_bubble_animated_no_badge fb_customer_chat_bubble_pop_in” style=”background: none; border-radius: 50%; bottom: 18pt; display: inline; height: 45pt; padding: 0px; position: fixed; right: 18pt; top: auto; width: 45pt; z-index: 2147483646;”><div class=”fb_dialog_content” style=”background: none;”><iframe name=”blank_f39e23aeefd7434″ width=”60px” tabindex=”-1″ data-testid=”bubble_iframe” frameborder=”0″ allowtransparency=”true” allowfullscreen=”true” scrolling=”no” allow=”encrypted-media” src=”https://www.facebook.com/v2.12/plugins/customer_chat/bubble” style=”border: none;”></iframe></div></div>
There you can see that position is fixed, though you may try to overwrite z-index or or botton/right position. You may overwrite is in any .css by class