这个句子本身是有问题的,因为since half a month ago表示持续了半个月,前面要用延续性动词.而buy（bought）是瞬时性动词,用在这里不正确,要改成buy的延续性动词have,整句话的正确写法：He`s had this backpack since half a month ago.
下面要改同义句,有两种改法：
时间状语since half a month ago 相当于 for half a month,于是整句改成He`s had this backpack for half a month. 改成It is + 一段时间+since+时间点的句式：It is half a month since he bought this backpack.注意这里since后面跟的是时间点,用瞬时动词buy. 有问题欢迎追问,
