H1B Cap-exempt - F1 to H1B Automatics, exit and re-enter US on F1?

My employer filed a petition for H1B on my behalf in 04/2018. I left the company in 06/2018 for grad school. The COS petition ended up getting approved on 10/5/18, pushing me from F-1 to H1B. Because my F1 visa was still valid back then, I left and returned US on 10/24/18 to regain my F1 status. The employer sent the withdrawal letter to USCIS on 10/16/19 so presumably I was on H1B status for ~10 days, from 10/5/18 to 10/16/18.

My question is: if another employer wants to sponsor me, can it file the petition claiming me as cap-exempt? I didn’t get the H1B visa stamp or worked during that 10 days as I was focusing on getting back to F-1. Can’t find anyone in a similar situation so that’s why I’m posting here.

It is slightly grey area…technically, they can file for H1B Transfer as cap exempt as you had H1B status at least once, irrespective of you were maintaining it or not…