H1-B transfer advice, talking to recruiters

[kpinn]

Hi all! I’m recently out of work and trying to find a new position. I tick no on my applications, whether i need a sponsorship but when i’m contacted for a phone screen and i tell them im on the h1b visa, i feel like I’m eliminated. I am already on the H1 and i would require a transfer, can you guys suggest of a way of how to talk to the recruiter to inform them clearly of my situation and how to convince them in a positive way so i can make it to the next round? Ps: I’m in construction/ civil engineering industry. Thanks so much!