As per IEEE 12207, who has to perform Software integration testing (SOIPL): SW Testing team or SW Development team?
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The TL;DR; answer is "It depends..."
ISO/IEEE 12207 doesn't specify teams as such, simply the processes to be followed. Depending on the nature of the activity (and other requirements, eg DO-178, IEC61508) which introduce requirements for independence at the higher levels, then a single person can be responsible for the whole life-cycle.
In simple terms, the Software Integration Process (of which integration testing is a part) builds all the (unit tested) modules into a single executable. The stages of the process will be as follows:
In a small project, the integration tester(s) may well be the same software engineer(s) who wrote the code... if you have separate teams, I suggest that start of the Software Integration Process is probably a good handover point, because thereafter you are testing a full build, probably on target hardware. But that is a local decision to be made.