Which is preferable, simple past or present perfect, in situations like this one: I had a conversation with my friend and we planned to do something; shortly afterwards I call him back to announce the accomplishments. My biggest doubt about simple past is that perfect aspect is used to indicate past action (accomplishment) with current relevance, at the same time I'm not sure if I'm allowed to use present perfect, because there's a gap between accomplishing and the current moment, which is a characteristic of simple past.
Look at the following sentences:
(a) Past simple: I lived in Florence for five years ... but I do not live there anymore.
(b) Present perfect: I have lived in Florence for five years ... and I still live there now.
(c) Past simple: I broke my glasses ... but it does not matter. I repaired them.
(d) Present perfect: I have broken my glasses ... and so I can't see properly now.
You probably learned the difference between (a) and (b) years ago: that one of differences between past simple and past perfect is the 'time' of the verb, i.e. when it happened. The difference between (c) and (d) is harder to understand.
In (c) and (d), 'time', i.e. when the verb happened, is not really what separates the two sentences; it is possible that both (c) and (d) happened last month, this morning, or one second ago. What is important is that the event in (d) is considered more relevant to the situation now than the event in (c), which is why it is given in the present perfect.