The answer is days, weeks, months or years, depending on (1) available manpower to perform examinations, (2) pending backlog of other casework/evidence to be examined and (3) how important the investigation is deemed in the eyes of managers prioritizing which cases/examinations are to be completed before others.

The forensic exams may be much more involved and time consuming than you might imagine. Even though police personnel may have told you an item was being collected for fingerprint examination, when experts finally begin detailed examination they may find fibers from clothing or gloves, hair fragments, minute blood splatter/smears, or other types of evidence which may require months for completion if all possible evidence is to be harvested utilizing various laboratory procedures (Trace Evidence, DNA, Latent Print Examination and more).

Think of the rocks as if they were clean and painted white instead of their current condition. Now imagine that you are holding a rubber stamp which you have just inked with ink from a stamp pad. If there are any surfaces on the rocks which might be smooth enough to enable reading some of the rubber stamp name/wording after you impress the stamp (gently or firmly), then there is potential that the rocks bear identifiable latent finger or palm print impressions.

Latent Print Examination procedures used to process/examine evidence are be tailored to produce, insofar as possible, contrast between latent finger/palm impressions and the evidence surface (as if the surface were clean and as if the impressions had been deposited while the fingers were coated with ink that would contrast with the surface).

Any surface that is about as smooth as the miniature corrugated cardboard type ridges on your fingers can potentially bear identifiable latent fingerprints... and the flexibility of the finger skin can often also conform to relatively rough surfaces such as imitation leather dashboards. Fingerprints from crime scenes have been identified on papers, cigarettes, fruit, crumpled aluminum cans, plastic garbage bags, bed sheets, dead bodies (prints on bodies are usually contaminated prints involving body fluids, lipstick or some other substance transferred via the suspect's fingers), and thousands of other surfaces. Fingerprints on paper, cardboard and unfinished wood can last for up to forty years (per actual casework histories) unless exposed to water (and contaminate transfer prints can even then sometimes persist). Fingerprints on non-porous surfaces such as plastic, metal and glass can last for years if not exposed to water and if left undisturbed.