Why I get error when trying to save an entity which include enum?

I have the following enum from a Spring Boot application and I have a problem with parsing probably.

import com.fasterxml.jackson.annotation.JsonFormat;
import com.fasterxml.jackson.annotation.JsonValue;

@JsonFormat(shape = JsonFormat.Shape.OBJECT)
public enum Month {
  JAN(0),
  FEB(1),
  MAR(2),
  APR(3),
  MAY(4),
  JUN(5),
  JUL(6),
  AUG(7),
  SEP(8),
  OCT(9),
  NOV(10),
  DEC(11);
  
    @JsonValue
    private final int value;

    Month(final int value) {
        this.value = value;
    }

    public int toInt() {
        return value;
    }

    public static Month fromInt(final int value) {
        switch (value) {
            case 0:
                return JAN;
            case 1:
                return FEB;
            case 2:
                return MAR;
            case 3:
                return APR;
            case 4:
                return MAY;
            case 5:
                return JUN;
            case 6:
                return JUL;
            case 7:
                return AUG;
            case 8:
                return SEP;
            case 9:
                return OCT;
            case 10:
                return NOV;
            case 11:
                return DEC;
            default:
                return null;
        }
    }

    public String toString() {
        switch (this) {
            case JAN:     
                return "JAN"; 
            case FEB:
                return "FEB";
            case MAR:
                return "MAR";
            case APR:
                return "APR";
            case MAY:
                return "MAY";
            case JUN:
                return "JUN";
            case JUL:
                return "JUL";
            case AUG:
                return "AUG";
            case SEP:
                return "SEP";
            case OCT:
                return "OCT";
            case NOV:
                return "NOV";
            case DEC:
                return "DEC";
            default:
                return null;
        }
    }
}

Here is entity which holding the enum:

public class Trip implements java.io.Serializable {    

  @JsonProperty("k1Month")
  private Month k1Month;
...
}

Here is when I'm doing the save in the Controller:

@PutMapping("/Trip/Update")     
public void updateTrip(@RequestBody Trip trip) {                            
  tripService.updateTrip(trip);     
}

I'm calling the Controller from Spring Boot webclient:

public static Trip saveTrip(Trip trip) {
  String url = TripcalculationsServiceApplication.Trip_APP_BASE_URL;
   WebClient client = WebClient.create(url);
   return client.put()
            .uri("Trips/Trip/Update")
            .body(Mono.just(trip), Trip.class)
            .retrieve()
            .bodyToMono(Trip.class)
            .block(); 
}

I receive a warning but I think it causing the webclient call to fail, here is the warning:

Resolved [org.springframework.http.converter.HttpMessageNotReadableException: JSON parse error: Cannot deserialize value of type com.mycompany.tripservice.entity.Month from String "JAN": not one of the values accepted for Enum class: [11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]; nested exception is com.fasterxml.jackson.databind.exc.InvalidFormatException:

The calling service throw an error 400 bad request (I'm thinking it is related to the parsing but cause only when I select the Month value the service failed).

org.springframework.web.reactive.function.client.WebClientResponseException$BadRequest: 400 Bad Request from PUT