Can phosphors exhibit stimulated emission? I read that phosphorescence is caused because of the presence of "forbidden" energy states. This causes the photon that is absorbed to not be immediately emitted like fluorescence but emitted after a delay. Fluorescent particles can be "forced" to release their energy by passing another similar photon in near vicinity, through stimulated emission. Can  phosphorescent particles exhibit stimulated emission?
 A: Yes, there is stimulated phosphorescence. 
Fluorescence and phosphorescence  are a type of luminescence. Luminescence is defined as spontaneous emission of light not resulting from heat.
Therefore, fluorescence and phosphorescence by definition are spontaneous emission (still, there is stimulated versions).
Photoluminescence is a type of luminescence, where light is emitted after the absorption of photons.
Fluorescence is a type of photoluminescence where it is a result of singlet-singlet electronic relaxation (for phosphorescence, it is triplet-singlet state).
Fluorescence occurs when an orbital electron of a molecule, atom, or nanostructure, relaxes to its ground state by emitting a photon from an excited singlet state.
You are correct, in case of phosphorescence, the emission does not happen right away after excitation, but with a delay. 
https://en.wikipedia.org/wiki/Luminescence
In the case of stimulated phosphorescence, they usually do two types of stimulation, Optically Stimulated Phosphorescence (OSP), where they use a laser to stimulate the material. They can use thermally stimulated phosphorescence too.
Please see here:


Immediately after illumination of quartz or feldspar samples by green light from a laser, there is phosphorescence (optically stimulated phosphorescence, OSP), with a lifetime of a few seconds, the size of the signal being dependent on radiation dose. For both minerals there is also charge transfer into low temperature TL peaks, the amount of transfer being dependent on dose.


https://www.sciencedirect.com/science/article/abs/pii/0277379188900376


To address and overcome the difficulties associated with the increased reactivity and susceptibility of blue emitters to deactivation pathways arising from the high-lying triplet excited states, we have successfully demonstrated an innovative strategy of harvesting triplet emission via the “thermally stimulated delayed phosphorescence” mechanism, where thermal up-conversion of excitons from the lower-energy triplet excited states (T1) to higher-energy triplet excited states (T1′) are observed to generate blue emission.


https://pubs.acs.org/doi/10.1021/jacs.8b09205
Though, it is very important to understand what stimulated emission is.


Stimulated emission is the process by which an incoming photon of a specific frequency can interact with an excited atomic electron (or other excited molecular state), causing it to drop to a lower energy level.


So in the case of phosphorescence, the process itself can be stimulated, the emission itself will be spontaneous.
