Hi
when you say, July to June. lets assume your fiscal year variant is July 2015 to June 2016 then fiscal year should be 2015. lets assume youare takeover date is Aug'2015. so, before you start Fixed Assets migration using AS91. you have to do below steps.
Spro--> AA --> Asset Data Transfer --> Parameters for Data Transfer --> Data Specifications -->
Specify Transfer Date/Last Closed Fiscal Year
Set date as 31.08.2015
Specify Last Period Posted in Prv.System (Transf.During FY)
Set FY 2015 and Period 2. so, system will start posting depreciation from 3rd month i.e. sep'2015. since, you have already migrated first 2 preriods.
hope its clear now.
Regards
Srinivas