Is there a word or phrase for these specific types of memories?

Forgotten memory - memories that are technically still there as signals in your brain, but where you've lost the ability to consciously recall it. They can sometimes be retrieved with aid or certain triggers.

Cued recall is the act of recalling such forgotten memories off a trigger.

The thing that causes you to remember that forgotten memory could be referred to as a memory trigger.

I think in this particular situation you should characterize your memory as dormant that can be roused or revived at a later date by a stimulus.

Another apt adjective is latent.

Googling the latter term yielded the following contextually relevant example sentence:

Otherwise we shall be compelled to believe that all our knowledge, all our store of images and memories, all our mental habits, are at all times existing in some latent mental form, and are not merely aroused by the stimuli which lead to their display.

Otherwise in cognitive psychology it is known as cue-dependent forgetting.

People speak of unbidden memories, those memories that flood into your mind spontaneously when evoked by a scent, a taste, a sound, a sight. So perhaps you could call these bidden memories, memories that require someone else mentioning something from the past in order for you to be able to bring it to mind.

Superior biographical memory or hyperthymesia is the common medical term.

Hyperthymesia - a condition in which an individual possesses a superior autobiographical memory, meaning he or she can recall the vast majority of personal experiences and events in his or her life. The term “hyperthymesia" is derived from the Greek words hyper meaning "excessive" and thymesis meaning "remembering".

Photographic memory can be used too. Although it is common to refer to it as remember everything you see you can also use it for other areas and it keeps the same meaning.

An ecphorized memory

Ecphorize (also ecphore) [fr. Gk ekphoros, (to be) made known] /EK fur ize/ Psychol. to evoke or revive an engram (an emotion, a memory, or the like) by means of a stimulus