After engagement can both partners talk to each other and respect to the boundaries of Islam?
Answer in the light of the fatwa of Ayatollah Khamenei.
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In the name of Allah, the most compassionate, the most merciful
I found a similar question/answer, which probably can help and solve your query. According to that similar question it almost asks about how much can we have relationship by internet (after engagement), so its answer is as following:
You must avoid of expressing the speech (words) which is the stimulant of lust or is appropriate for canonical (Shar'i (شرعی)) husband and wife.
Consequently, it can be inferred from the mentioned Fatwa that you must not talk in the way which can stimulate the lust, then you can just talk in common ways as if you are not Mahram to each other (although you are not mahram to each other if you have not recite the Shar'i-Sighah of that.
Nevertheless, you'd better refer to the source below for more accurate answer: