PA landlord tenant act, in writing requirement of PA 68 PS section 250.512(e)

Following the termination of our lease, the landlord took 46 days from the date of termination, and 61 days from our move-out date to provide us with the detailed list required by §250.512(b). However, we did not inform the landlord on paper of our new address - we used email, as the landlord had verbally requested that all communications be handled through email "so that there is a paper trail for both of us" (paraphrasing their words.) The landlord replied to the email, acknowledging receipt, a few days after our move-out, so there is no question as to whether they received it or not. We received no further correspondance until this week, when I emailed the landlord asking for our deposit, and she physically mailed me an invoice for several thousand dollars of alleged damages. Now, if I'm reading the law correctly, because the landlord took more than 30 days to provide an invoice, §250.512(b) protects me from any claims of damage, and (c) entitles me to receive double my deposit back. So, is there clear precedent for email meeting (or not meeting) the "in writing" requirement of (e) for notification of my new address?