Officially the parent should apply for a school place through the Local Authority where they are currently living. However, as they are clearly there on a very temporary basis and they plan to move into Bucks almost immediately, then I would have thought that Bucks CC Admissions might be willing to deal with the application from the outset. (I think this is where the misunderstanding has arisen.)
Regardless of that point, the parent needs to apply for immediate 11+ testing. I believe that this may be the appropriate form, but she should check with Admissions: http://www.buckscc.gov.uk/assets/conten ... _Final.pdf
The child should then be invited for testing within a month.
It is slightly unfortunate that they have chosen High Wycombe this year because most of the the grammar schools there are far more over-subscribed than in previous years, and even if the child qualifies in the 11+, they may not receive a convenient school place. This gives a picture of how things stand at present: http://www.elevenplusexams.co.uk/school ... n-profiles