Step 1 (Identify the voice of the given sentence).
The sentence "She has preserved all the old letters of her dead lover"} is in the active voice, where the subject ("She") performs the action ("has preserved") on the object ("all the old letters of her dead lover").
Step 2 (Recall the rules for changing to passive voice).
In passive voice:
1. The object of the active voice becomes the subject.
2. The subject becomes the agent, usually introduced by "by".
3. The verb form changes to its passive equivalent.
4. The tense must be maintained — here, "has preserved" (present perfect) becomes "has/have been preserved".
Step 3 (Determine correct verb form).
Since the new subject "all the old letters" is plural, we use "have been preserved" instead of "has been preserved".
Step 4 (Construct the passive sentence).
"All the old letters of her dead lover" (new subject) + "have been preserved" (passive ver(b) + "by her" (agent)
\underline{All the old letters of her dead lover have been preserved by her}.
Step 5 (Verify).
The meaning and tense remain unchanged, and the construction follows the passive structure correctly.
\[
{\text{All the old letters of her dead lover have been preserved by her. (Option (a)}}
\]