I hope my research on this might help....but please don't take this as definitive. No doubt there are others here that will understand this issue better, but this is my attempt at understanding the regulations:
A helicopter piston engine is said to be being maintained ‘on condition’ when the engine (whatever its hours) is outside the 12 year + 20% rule, after which the engine must normally be fully overhauled. This means it can only be used for ‘private use’ - for airworthiness purposes and not for ‘public transport’ or ‘aerial work’.
The regulations that I have found that relate to this are as follows:
1. Air Navigation Order 2009 Paras 3.1.1 and 3.1.2
"A flight is for the purpose of aerial work if payment is made in respect of the flight or the purpose of the flight, unless the flight is in fact for the purpose of public transport. If the only payment involved is the payment of the pilot, the flight is deemed to be private for airworthiness purposes (although it will still be aerial work for other purposes, e.g. flight crew licensing). This enables a private owner to pay a flying instructor for a flying lesson in the owner’s aircraft even though the continuing airworthiness requirements that would be applicable to public transport aircraft may not have been applied. “
So, as I understand it, so long as the aircraft is privately owned, then the owner can pay an instructor to train him or her on it whilst it is being maintained 'on condition'. So far so good.
2. Air Navigation Order 2009 Paras 6.5.2, 6.5.3 and 6.5.4 - Jointly Owned Aircraft
"An exception has been established so that the continuing airworthiness requirements applicable to public transport aircraft do not have to be complied with. This is provided -
(a) payments are made by members of the group to a central fund which amount to no more than direct and annual costs of operating; and
(b) the group comprises no more than 20 persons (each with at least 5% share) whose names have been notified to the CAA.
This exception applies whether the aircraft is jointly owned directly by no more than 20 persons or by a company which is owned by no more than 20 shareholders. The shareholders must be individuals and not companies. It should be noted that this exception can only be relied upon if the only payments are those made within the group relating to the direct and annual costs of operation. No other payments can be made if it is wished to rely on this exception. In particular, a member of the group cannot pay an instructor to train the group member in the group-owned
aircraft.
So the same aircraft could be owned by a company or group, with up to 20 shareholders. But any member of the group cannot rent it out or pay an instructor for PPL training. In other words, this seems to say that an owner could only pay for instruction on the aircraft if he/she was the sole owner of it (point 1 above) but not if he/she is a joint owner.
I hope this may help!