since与after 都可以用来引导表示从过去某一点开始的时间段词组.它们的不同之处在于：
a）since引导的词组所表示的时间一直延续到说话时为止,因而要与现在完成时连用.例如：He has been there twice since 1982.I have done nothing since six o”clock.
b）after引导的词组所表示的时间是纯系过去,并不延续到说话时,因此要和一般过去时连用.例如：He went home after school.
因此,这里应该填since,而不能填after.
另外,since moving to China,这里把since 看成介词了,since+doing 也就可以了.构成了介宾短语.
实际上该句子应该为：
I have been back twice since I moved to China.
省略用法后,才成为：
I have been back twice since moving to China.