Is it a condition for memorizing the Qur’an to recite it by heart with diacritics?

There is no requirement for the memorized Qur’an to be vocalized (i.e., contain diacritical marks). The Companions memorized it without a vocalized Mushaf, and it is inconceivable for someone reciting from memory to be bound by vocalization. However, if "vocalization" refers to observing the grammatical inflections (harakat al-i'rab), then this is obligatory when memorizing and reciting from memory.