Would appreciate some help on this...

Will be flying tomorrow Sun 17th from PHX via LAX to ARN.

PHX - LAX arrives at T7/8, and LAX - ARN departs from TBIT.
Transfer 1 h 39 min only. SK 940 departs at 2 pm-ish.
Traveling on same ticket.
Luggage checked in all the way.

Question - how do I best get from T7/8 to TBIT given the short transfer? I think I can find my way through the airside link from T7/8 via T6, T5 and T4, but it is not clear for me if I still need to clear TSA at TBIT.
Is there a true airside link all the way to TBIT? Where do I enter TBIT in that case?

Thanks.