This doesn't seem possible unless you roll the funds from the first HSA to the new one ...
From the IRS :
For HSA purposes, expenses incurred before you establish your HSA aren’t qualified medical expenses. State law determines when an HSA is established. An HSA that is funded by amounts rolled over from an Archer MSA or another HSA is established on the date the prior account was established.
https://www.irs.gov/pub/irs-pdf/p969.pdf
