How to transfer colllider from OnTriggerEnter to Update

you can try this, it will make sure that lastcollider is not returned from update() unless it has a value.

  using UnityEngine;
  using System.Collections;
  
  public class testtrigger : MonoBehaviour {
  
      Collider lastCollider;
 
      void OnTriggerEnter(Collider other){
          lastCollider = other;
          Debug.Log (lastCollider);
      }
      // Use this for initialization
      void Start () {
      
      }
      
      // Update is called once per frame
      void Update () {
         if(lastCollider != null)
         {
          Debug.Log (lastCollider);
         }
      }
  }