It depends how you'll model it in Caesar.

If you model the tee separating the tee's branch and run short-length spools from the connected pipework using tee actual thickness (S-80, higher than S-40 pipe thickness), then matching pipe thickness is S-80, because the SIFs/SSIs are calculated for the S-80 pipe thickness and the nominal stresses evaluated for S-80 pipe spool are amplified for SE/SL assessment.
This is the most accurate and realistic approach - your (2) clause above, I believe...

There is indeed option (3) - apparently simpler but actually inaccurate...to let thickness un-changed at S-40 and to specify SIFs/SSIs for S-80. Please note that maybe SIFs/SSIs are calculated correctly, but they are used to multiply the nominal stresses calculated for S-40...and this is incorrect. This is your option (3), I believe...

I said "apparently" simpler because second approach requires to calculate SIFs/SSIs separately. For the first method, SIFs/SSIs are correctly evaluated by Caesar using the actual S-80 thickness...unless you intend to use B31J formulas without FEA Tools employment.

Be careful how you define the tee. Is it a reduced tee, or an equal one? If it is a reduced tee and you want anyway to use option (3), and the SIFs are calculated as per B31.3 App. D, then you may specify the intersection type ("3" for B16.9 welding tee). If the SIFs are calculated as per B31J, you shall NOT specify the intersection type. Otherwise Caesar will alter the stresses on branch side using the effective section modulus, and this is wrong, against B31J philosophy. However, in this case, you need to specify properly "in-plane" and "out-plane" values, depending on branch and run orientation with respect to coordinate axes - see Caesar II User Guide for details.