If the engine has gone "on condition", the only person able to learn on it is the sole owner or members of their immediate family.
If it is not yet on condition, anybody can learn, or be tested on it.
Unless the instructor does it for nothing, in which case it's all fine. Historical reasons.
This changed with the introduction of EASA and Part M some years ago. For EASA aircraft on a C of A or Permit to Fly, as a sole owner
or joint-owner he can receive remunerated training towards issue, renewal, and revalidation of a licence, rating, or certificate on that aircraft.
See
AIC W001/2011 paragraph 2, and the flow chart at the end.
The rules are different for non-EASA aircraft which are regulated by the ANO: information about learning to fly in a LAA Permit to Fly aircraft is available in
Technical Leaflet 2.09.
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