Do '之后' and '后位' have the same meaning?
...之后 is a normal term to express "after...". So,  葬礼之后 is correct in this context.

后位 is short for 后面的位置. It refers to positioning, not timing sequence. It is only used in some particular areas. Someone had given enough examples above. 

后位 could also be understood as:

皇后之位 in 宫廷剧 （Chinese royal opera);

Another 后卫： the back (defense position) in sports: soccer, American football, and etc.