I've never had cause to try, but you could certainly give them a call and ask. I would be surprized if they allow it though, since the reality is that you are not the current software license holder of record, the owner of the AppleID used to purchase the license is.
Keep in mind that your fellow empolyee did not buy the software, she merely purchased a license to use the software, and the only record of that license issuance is tied to her AppleID, not anyone elses. At the very least, I would imagine it would have to be she who requested a transfer of license, not someone else.
All they can say is no, so if you think it worth pursuing, then sure, give Apple a call and ask.
For information only, below is the limits of the license agreement you sign when making a purchase in the App Store (this is from the USA web site document). Note that the licenses are explicitly non-transferable, which is why I say I doubt Apple would make any exceptions to the rule.
"a. Scope of License: This license granted to you for the Licensed Application by Licensor is limited to a nontransferable license to use the Licensed Application on any Apple-branded products running iOS (including but not limited to iPad, iPhone, and iPod touch) (“iOS Devices”) or Mac OS X (“Mac Computers”), as applicable (collectively, “Apple Device(s)”) that you own or control and as permitted by the usage rules set forth in the Mac App Store, App Store and iBooks Store Terms and Conditions (the “Usage Rules”). This license does not allow you to use the Licensed Application on any Apple Device that you do not own or control, and except as provided in the Usage Rules, you may not distribute or make the Licensed Application available over a network where it could be used by multiple devices at the same time. You may not rent, lease, lend, sell, transfer redistribute, or sublicense the Licensed Application and, if you sell your Mac Computer or iOS Device to a third party, you must remove the Licensed Application from the Mac Computer or iOS Device before doing so. You may not copy (except as expressly permitted by this license and the Usage Rules), decompile, reverse-engineer, disassemble, attempt to derive the source code of, modify, or create derivative works of the Licensed Application, any updates, or any part thereof (except as and only to the extent that any foregoing restriction is prohibited by applicable law or to the extent as may be permitted by the licensing terms governing use of any open-sourced components included with the Licensed Application). Any attempt to do so is a violation of the rights of the Licensor and its licensors. If you breach this restriction, you may be subject to prosecution and damages."
