Your pre-purchase inspection report mentions the presence of cracks in the foundation and recommends an expertise on the subject. While a buyer usually has only a few days to review the report and make a final decision, the reality is that it is not usually possible to determine the active or stable nature of a foundation crack in a single assessment.
To determine if a crack is active or not, it must be evaluated over a period of time, monitoring whether or not it is expanding. To monitor the situation, one way is for the expert to measure the activity of the crack by installing a fissurometer on it to periodically read the width of the crack over a period of time. Another method is to seal the crack with plaster or cement and then check for further cracking. To distinguish a minor shrinkage crack from a major structural crack, the expert must also measure the amount of differential settlement (i.e., the amount of settlement of the foundation) by taking a reading with a laser level. A maximum differential settlement of 20 mm (3/4 in.) and an absolute of 25 mm (1 in.) is considered tolerable for a residential building.
If you want to check if the crack extends the full height of the wall, but the foundation is not visible from the inside, you will have to dig an exploratory trench on the outside of the foundation. Take the time to have a complete survey done, as the results could make the difference between simply needing to repair the cracks with injection and having to stabilize the building with piling, which will cost tens of thousands of dollars. But regardless of the type of crack, repairs must be made to prevent water infiltration into the house.