Jacob does not tell us how much time passes between his account of receiving the plates from Nephi and Nephi's death. There is a possibility that Nephi could have lived for some time after giving the record to Jacob.
While that is a possibility, it is not a strong one. We have examined the ending chapters of 2 Nephi and noted that 2 Nephi 32 appears to be abbreviated. The suggestion was that this was due to failing health, and the desire to end with a final testimony. Nephi specifically notes in verse 14 of 2 Nephi 33 that "I speak unto you as the voice of one crying from the dust." This reference to Isaiah is probably in the original context of words from one who had died and lies in the grave. The indications are that Nephi senses his impending demise.
The next piece of information is that Nephi arranges for succession. First he makes sure that there is a transmission line for the small plates, and then a formal transmission of rulership, and not coincidentally, the large plates. These are the actions of a man preparing for the end, not one assuming several remaining years. While there is likely some time between the transfer of the small plates and the anointing of a new king, the time is probably measured in months, not years.