It was a matter of -------- would take the position.A.who B.

whoever多数情况是表示“无论谁、不管是谁”的意思.
不过：
whoever可以作pron.(引导名词性从句)表示“谁”,相当于"the person who”、"who that",即既要在主句中担任主语或宾语,又要在从句中担任主语.同理担任宾语用whomever.如：
Whoever（The person who/Who that） wants the book may have it.
谁想要这本书都可以拿.
I'll take whoever(the man who/who that) wants to go.
谁要去我就带谁去
所以：It was a matter of whoever(who that)would take the position问题是谁将坐上这个位置.