Here is a way to do it :
First, you need to extract the firepack_id you need to look for, then you need to loop through $arr1 and check if Firepack_sn is the same than than one of the firepack_id you extracted before, if yes, then you add it to an array.
$arr1 = json_decode('[{"Firepack_sn":"20012205","Installation_Date":"","Type":"EH","Standard":"VAS","Capacity_m3h":"81","Pressure_bar":"3,4","Rpm":"2930","Power_kw":"72","Pump_Type":"KSB KFP50-200","Motor_Type":"DOOSAN PU066 VAS/CEA","Controller_Type":"WB882-E10 VAS","Pump_sn":"085259","Motor_sn":"EARPA209635","Controller_sn":"","Servicelevel":"","Cust_id":"0","Cust_branche":"","Cust_name":"","Cust_address1":"","Cust_zipcode":"","Cust_city":"","Cust_country":"","Cust_Phone":"","Cust_coachlevel":"","Site_Name":"E-set","Site_address1":"","Site_address2":"","Site_address3":"","Site_zipcode":"","Site_city":"","Site_country":"","Site_contact":"","Site_phone":"","activated":"1"},{"Firepack_sn":"20023901","Installation_Date":"","Type":"DH","Standard":"VAS","Capacity_m3h":"195","Pressure_bar":"4,2","Rpm":"2000","Power_kw":"72","Pump_Type":"KSB KFP50-200","Motor_Type":"DOOSAN PU066 VAS/CEA","Controller_Type":"WB882-E10 VAS","Pump_sn":"085259","Motor_sn":"EARPA209635","Controller_sn":"","Servicelevel":"","Cust_id":"0","Cust_branche":"","Cust_name":"","Cust_address1":"","Cust_zipcode":"","Cust_city":"","Cust_country":"","Cust_Phone":"","Cust_coachlevel":"","Site_Name":"D-set","Site_address1":"","Site_address2":"","Site_address3":"","Site_zipcode":"","Site_city":"","Site_country":"","Site_contact":"","Site_phone":"","activated":"0"}]');
$arr2 = json_decode('[{"user_id":"40009","firepack_id":"20012205","activated":"1"},{"user_id":"40009","firepack_id":"21020393","activated":"0"}]');
$firepackIds = array();
foreach($arr2 as $item){
$firepackIds[] = $item->firepack_id;
}
$goodRows = array();
foreach($arr1 as $item){
if(in_array($item->Firepack_sn, $firepackIds)){
$goodRows[] = $item;
}
}
echo json_encode($goodRows);
Hope this helps.