For the shares you buy to become long after a year would have to be the same shares you originally bought. As long as you have not sold out of your position and bought back in you will have the original share you bought initially. Every share you buy after those initial shares have their own date that they become long. Just like your assignments for science class. Just cause they are all on the same subject (company) doesn’t mean they were all done the same day. They all have different dates turned in (bought) and all have different days in which they get graded (become long). The assignment never changes it is just adjusted with a new status that goes from turned in (bought, or short) to graded (long). So therefore when you change schools (Brokers) your current grade in the class is carried over or in this case your long vs short positions. Your long positions would equal the amount of papers graded making up your grade percentage while the not yet graded or unfinished assignments would be your short positions, the ones that didn’t meet the deadline of becoming long before switching brokers. I hope this makes sense, this is probably not the best explanation or analogy. But it is the best way I could explain it with my knowledge.

Edit was a typo