I'm confused by the use of かける in the sentence :
I thought かける was used to express an activity on going, which gets interrupted by something else. eg 話してかけて、雨がふりました。（it started raining whilst I was talking).
But here it seems like that second clause is saying: an conversation with a foreign friend came up with, which had already been ongoing. To me that doesn't make sense, because how can the conversation have already been in progress if it just 'came up' (ie because of the きた conjugation). Is that really the intended meaning here?