Is this a SFU thing as can find no reference to it on google or Trek Wikis
See this
Memory Alpha page, way down in the "Establishing Technology" section.
The 1991 reference book Star Trek: The Next Generation Technical Manual (pp. 123-125) explain the inner mechanisms of a phaser in more elaborate detail. Phaser is, according to the book, the acronym for phased energy rectification – named for the process of turning stored energy into an energy beam without an intermediate transformation. Energetic plasma is pumped to a prefire chamber made out of a superconducting lithium-copper. There, it undergoes a rapid nadion effect in which strong nuclear forces are liberated. A protonic charge forms and is released in pulses to the emitter made out of the same superconductive crystal. A beam of elecromagnetic energy is released from it, at the speed of light. On starships, energy for phasers originates from the EPS, while on hand units, the charge of energetic plasma is stored into sarium-krellide. This material is used because it can't accidentally release the charge of plasma.
Dialogue in the 1991 episode TNG: "The Mind's Eye" concerning the internal mechanics of a type 3 phaser rifle confirm, canonically, all the elements as they were established in the Manual. However, in Star Trek, phasers have been regularly used while starships travel at warp speeds, so the beam must also be traveling at faster-than-light velocities. Beginning with the 1993 episode TNG: "Inheritance", instead of being labeled as EM weapons, as the reference works have stated, phasers have been consistently referred to as particle beam weapons on screen. This information was also included in the 1994 Star Trek: Voyager Technical Manual - Writer's Guide, and has been corroborated in such episodes as "Time and Again", "Memorial" and "Endgame".
Even though the phaser beam was canonically established as not a beam of pure EM energy but a particle beam of nadions, the 1998 reference book Star Trek: Deep Space Nine Technical Manual still goes on to describe the phaser beam as an EM energy beam. According to page 84 of the Manual, a phaser beam can be delivered at warp speeds due to an annular confinement beam jacket and other advances in subspace technology. These are stated to be new inventions in the late-24th century. However, considering that first on-screen uses of phasers at warp occurred as early as the first season of The Original Series, this timeline for the invention would be inconsistent with canon. Furthermore, according to page 92 of the Manual, when phasers are fired by a ship with deflector shields active, the beam is frequency locked to the second-order harmonics of the shield emissions. This prevents the beam impacting on the shields and overloading them, or rebounding back at the firing ship.
See also
this nerdy and
this very nerdy thread.
Realistically, since "what is on screen is canon", and they show, with no obvious degradation effects, phasers firing at warp (See TOS, TNG, DS9, VOY; ENT used similar but different weapons but should be included; not sure if it was seen in TAS or not, that'll be my project for the weekend), firing phasers at warp, therefore, is canon.
The only reason why it would not be possible is if the phaser's ability to fire was removed (e.g. damage, loss of power, etc.). See ST:TMP (the deal in TMP wasn't that they could not fire at warp, but was because there was no power to fire them).
Now that it has been established that it can happen, we need to establish the range - the common theory being that once the beam is no longer within a warp field it would return to "normal" speed. This theory, therefore, would suggest that the range is limited to the warp field size of the firing vessel, and if the target's warp field is touching or within the firing ship's field, the range is extended to include that field (or fields - under this theory it is possible to "daisy chain" a phaser shot through multiple fields to reach its target) until the phaser's own "natural" range is met. This theory I like; however, may be difficult to implement and confusing/frustrating to those that don't understand.
I personally recommend that all weapons be unavailable (or extremely limited in range and accuracy) during warp flight for the firing vessel, and extremely inaccurate when firing at a vessel at warp (whether the firing vessel is at warp or not). Further, the effects imposed during warp should last for a short duration following the warp event. This will make the playing field more level in MP match ups, and reduce the instances of Warp in and Alpha (Picard Maneuvering) or Warp-Alpha-Warp (SFC3 warp-hopping). To make it believable, just say that the firing control gets wonky when at warp or dealing with vessels at warp, and while it is (or is not, whichever way SFC4 goes) possible, the effects are so reduced it isn't worth the effort, until fire control un-wonks itself.
The Czar