To further evaluate the situation, several clarifications would be needed.
a) What mod was reportedly installed by the shop?
b) Is it possible to attain a shop-issued battery for comparison and testing?
c) What is the condition of the damaged second battery?
Moving forward, a physical comparison of the batteries sold at the shop and the remnant battery would be needed. 18650 type cylindrical lithium cells often vary in cell wrapping, laser etches, and stamping. Past the aesthetics, 18650 type cells have a wide range of construction methods and cathode/vent (top of the cell). The physical dimensions (length, diameter) can be used to identify a specific cell. The top of a cell can feature several different variations of CIDs (current interruption device), or be unprotected. Using these methods is generally sufficient in identifying different cells. If further investigation is required, the cell could be taken apart and internal components measured.
To determine if the device had been modified, we would need to define what it means to modify an e-cigarette in this case. If changing the battery cell is a significant alteration to the shop’s mod, would something noticeable have been broken such as a sticker or label? If we are looking for a mechanical mod, we can compare the mechanical structure to a new e-cigarette and trace the circuitry to see if anything has been added or removed in the path of current. A thorough examination of the shop’s mod is required for this determination.