Citation XL First Officer reported on climb out they encountered a loss of oil pressure in the right engine resulting in the shutdown of the engine and cabin fumes. Flight crew returned to departure airport and landed.

Narrative

On Day 1; I (as First Officer) dutied on at XA:30 am local to reposition Aircraft X from ZZZ to ZZZ1. (The day earlier; on Day 0; we had been in a different aircraft and we were supposed to reposition from ZZZ2 to ZZZ1; however; we were forced to divert back to ZZZ2 due to a pressurization issue with the aircraft. On the evening of Day 0; the company had us drive from ZZZ2 to ZZZ; we had minimum rest; and we dutied on the following morning to reposition Aircraft X to ZZZ1.) We completed our 'aircraft acceptance' of Aircraft X on the morning of Day 1; and that comprised a thorough preflight check and document review of Aircraft X. We concluded that the aircraft was airworthy and legal to make said repositioning flight. At approximately XC:50 am local; we commenced our takeoff roll on RWY XXL; and we were cleared via the ZZZZZ RNAV Departure; ZZZZZ1 transition. During the takeoff roll; we smelled an unusual aroma -- one similar to WD40 -- however we thought that this was the result of the maintenance performed on the aircraft prior to our assuming this aircraft. We thought that the aircraft had been in maintenance for a trim issue; however; we soon found out that that was not the case. At approximately 4000 feet; while on the turn in the departure procedure; we got: the Master Warning; Lo Oil Press R annunciator; R oil pressure tape dropped to zero; smoke in the cockpit; and we performed a precautionary right engine shutdown and [requested priority handling]. We successfully returned to ZZZ; and the Airport Rescue and Firefighting (ARFF) team members were able to assess that our aircraft was not in danger of catching on fire and that we were safe to taxi back to the FBO on one engine. Once back at the FBO; the ARFF and airport authority personnel asked about our situation; as they stated that this very same situation had occurred in this very same aircraft in the recent past. We were stunned to hear this news. We proceeded to fill out our required paperwork; and after asking the Chief Pilot if we should fill out reports due to this event; he stated that there was no need to do so. A couple of days after this incident; I learned that this aircraft had not flown since it's last incident 9 days earlier. From second-hand information obtained by other company pilots that contacted me; this aircraft had a mere cursory inspection of the right engine after the first precautionary shutdown 9 days earlier. Apparently; the right engine had not been run-up past idle thrust after the first precautionary shutdown -- although this was second-hand information.In compliance with our Chief Pilot's guidance; neither me; nor the Pilot Flying (and PIC); filled out reports; however; I now feel that this was in error; as this was the prime example of when to fill out a report. After the stress of this situation; followed closely on the heels of the prior day's pressurization issue in another aircraft requiring an immediate return to the airport; followed by minimum rest and very little support from our company; we trusted the guidance of our Chief Pilot to NOT submit reports. I learned that the crew from 9 days earlier DID fill out reports; and their events mirrored ours. I am SCARED that we were placed in an aircraft that had NOT had the appropriate maintenance performed after the first precautionary shutdown; and I am afraid that our company placed monetary gain over the safety of the flight crew.