Thanks Rodolfo, for your advice!
Yes, the SMSESSION's function is clear to me. The point is, I would expect that it is sent from the server upon the request to the start page, http://server.com/carambaLS1/. But this request is not recorded, it is simply missing in the script. If I add it manually, it does not receive an SMSESSION when called. Instead, it gets something like 421-byte request headers for "https://server.com/s/SmMakeCookie.ccc?SMSESSION=QUERY&PERSIST=0&TARGET=... - you see, the SmMakeCookie function is called to get a SMSESSION, but in the subsequent web_url calls still only the SMSESSION=QUERY comes, no real SMSESSION.
I have understood that I have to comment out the cookie as it was recorded. That session is timed out in replay time.
Any suggestions would be appreciated...