Finally the wait for the Xperia Z1, Z1 Compact and Z Ultra users is over now. Today Android 5.1.1 Lollipop firmware with the build number 14.6.A.0.368 was certified over PTCRB for the Xperia Z1, Xperia Z1 Compact and Xperia Z Ultra. This build number has been certified across most of the variants for each device such as Xperia Z1 (C6902, C6903, C6943, C6906), Xperia Z Ultra (C6802, C6833, C6843, C6806) and Xperia Z1 Compact (D5503). We can guess this firmware update has a full fix for the Stagefright vulnerability.
Xperia Z1 Compact
Xperia Z Ultra