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It does not fit 62mm rim. It is too small for that, and it is too large for 58mm. So it would fit lenses with 60mm rim. I think 135mm f2.8 lens has 58mm rim, and retractable lens hood. So it should fit that lens model with the hood. 

Cap has been used, but it is in good condition. It has some scratches from use. 
It will be shipped as pictured without any accessories. I will pack it well to protect from damage during transportation. 
 This cap is fully operational and functions as intended.  I would rate it an 8, on a scale from 1 to 10.