LEO rifles have to be made/built completely by a C-2, and cannot be pieced together. Read the BATF listing on LEO rifles.
As for a LEO SBR, Per BATF the LEO SBR needs to be built by a C-2 then transferred to the Department on a Form 5 for a tax-free transfer.
As for SBR'g a pre-purchased department owned LEO rifle, again, the rifle belongs to the department until it is gifted to you on retirement, even if you bought the rifle on an individual Ofc letterhead. You can SBR a weapon that is personally belongs to you, not bought threw department on department letter head, but it still needs abide by the AWB due to not being department property/issue.
The down and dirty is to take the LEO rifle to a C-2, have Him install the SB, and register/transfer the SBR LEO weapon back to the department on a form 5. When the rifle is gifted to you at retirement, either pull the Short barrel (remove the SBR from the NFA registry), or have the LEO SBR rifle gifted to you, then Transferred to you on a form 4 ($200 tax stamp) from the department.
Once gifted, the rifle belongs to you, and is no longer connected with the department as a issued weapon (even thought you paid for the rifle out of your own pocket from the start).