Air conditioning shuts down after a few minutes when outside temperature is approx. 25°C

Hello together, For some time now the air conditioning of the Musa 2007 1.3 Multijet 90 HP is switched off when the outside temperature is very high. Sorry the question also in the FIAT forum because Musa and IDEA are almost identical. The 2-zone air conditioning goes on convection air and stays there. After a few minutes wait the air conditioning can be restarted (see the running belt wheel). Climate service was carried out to ensure the correct coolant level. The workshop said it w äre the compressor – costs in CH approx. CHF 1200 for the compressor (which I can’t believe). Who knows the topic ? Think it might be due to the dryer, pressure switch or sunlight sensor, as the compressor runs at least 10 minutes without problems.