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Etheral invokes power at the start of the movement phase.
All units within 12" benefit from the power "until the start of the Ethereal's next movement phase".

So yes, the unit could move away and still benefit as they retain the ability until their next movement phase. The only thing that stops it is if the Etheral dies (say, friendly fire from a blast or something before the buffed unit shoots).
Likewise though a unit that moved to within 12" of the Ethereal after the power is invoked would not gain the benefit from my reading of it.
In the case of Storm of Fire it would also apply to overwatch shots during the enemy turn so long as they haven't killed the Ethereal by that point..

Storm of Fire can only affect a unit "once per turn, regardless of how many Etherals invoke it". I read that as they can't get the extra shots twice in the same turn if they could somehow fire twice in one turn. Do note however that turn means player turn unless specifically stated as game turn so you can get the extra shots once in your turn and once in your enemies turn if firing overwatch.

*edit*
I suppose my interpretation of this is hinged on the power being "invoked" as being a one time thing that adds the buff to all units within range at that instant. Something being "invoked" is not defined in the rule book. I would treat it like a buffing psyker power even though it doesn't say it is (it doesn't say anything about what it is). One could interpret it as a sustained bubble of influence instead of a one-time application in which case the unit would have to be within 12" when it wants to use the benefit. Moving out would cause the unit to lose it. It does say that all units within 12" benefit from the power until the start of the Ethereal's next movement phase and not that all units within 12" benefit from the power and the power itself lasts until the start of the Ethereal's next movement phase.

 Vector Strike wrote:
Would it work with units inside transports when the Ethereal uses this ability?

Do models inside transports count as being on the table? Last I checked it was a no but I believe the last time I checked was 5th so I could be wrong (don't have my book handy).
How RAW looks to me is if they are in transports they are not technically on the table so they cannot be within 12" of anything so they cannot get the buff.

HIWPI: they get the buff if they are in the same transport as the Ethereal. They do not get the buff if they are in another transport.

An Ethereal inside a transport can invoke and use the hull to measure the 12", I'm not arguing against that. I was referring to a unit inside a transport apart from the Ethereal being buffed. That is what I assumed Vector Strike's question was about.

If an Ethereal invokes a power, whether outside or inside a transport, and an occupied transport is within 12", does the buff apply to those models inside the transport?

I'd say no as they are not physically on the table so cannot be within 12".

Page 78 grants special permission for the Ethereal to use his power but not special permission for that power to apply to a second, separate, transported unit.