When migrating a question as a moderator using a desktop browser, I can select a target site from the suggestions by typing into the "belongs on another site" field (moderators can migrate to any site in the network; normal users are shown a site-wise set list to select from):
In the mobile browser on my phone (Firefox 56.0 on Android, also tested it with Google Chrome 56.0 on Android), I am not shown any site suggestions when typing:
It is therefore not possible for moderators to migrate questions on mobile.
Update: As Cai figured out, the issue seems to be that the pop-up is not being re-fit to small screen sizes, making the suggestions appear somewhere below the close dialog, in a position that is inaccessible from my device (I can not zoom out or scroll down further than shown in the screenshot). The required fix for this issue then seems to be to make the close dialog fit on mobile devices, so all the buttons and fields can be accessed.