I listened to the music for a while, having written an important letter.

1b00Having written an important letter02b00, I listened to the music for a while.02br
00I listened to the music for a while, 01b00having written an important letter02b00. 02br
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00My grammar book says the second one is written to "emphasize" the participle pharse("having written an important letter"). But I learned from other book that if the participle pharse happens first, it should be put in front of the other sentence, just like my first example above.02br
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00What do you think about it? Is the second example correct or wrong? Thank you for your answer.0-