Part 107 UAS pilot reported briefly flying within an active TFR without authorization.

Narrative

I was in Location A to get video shots of the stadium on the day of a game. A colleague of mine had submitted for LAANC via Airloft. We received a clearance to fly just outside of the TFR. The exact incursion was taking off my UAS from within a TFR by about one city block and then accidentally flying further into the TFR. About half of my flight was in the TFR and half was outside from further away. The exact details are as follows; when we went to the location of what we thought was our permit; Airloft did not show the exact markings of the TFR. I parked my car at a Middle School thinking that this is where our permit was for. It is a nice open space without many people. We checked Airloft and we did not see the red circle over where we were. In reality; it looks like we should have parked at the Elementary school about half a mile from the Middle. I took off the drone and was just inside of the TFR but I thought I was outside and operating within the limits of our LAANC. The mistake was two-fold: 1) Not ensuring I saw where the TFR was upon take off. This was caused by either Person A's phone or Airloft malfunctioning and not showing the red. Normally our location is shown on the map as well as the red TFR. 2) Misunderstanding the map of the area. I understand that I was in the correct school but didn't realize that there were three different schools.There were no near misses; collisions; accidents or anything dangerous that happened. Safety was never compromised. As a handling; we have now realized that our app can glitch and will restart if there is not TFR data showing. Up to this point; we've never had a failure. Additionally; I will make sure I'm in the correct physical location at point of takeoff.