I believe the issue is that the JSON Path does not contain the target array name. Also, the Array Index should not contain the array name, but an integer index. Alternatively, you can set the update type to Append to avoid having to specify the index. For example:

Thank you so much, it works!

I just have an additional question. Do you know why, when I look at json text resulting from this transformation, the inserted value has double quotes.

Unless FME is completely certain, it has a tendency to default to string data types, which is why you get the double quotes.

You can cast (force) the values to int by using the following expression in the JSONUpdater:

ok thank you for this explanation