OLE DB provider "SQLNCLI11" for linked server failed to install INSERT

I have currently set up a linked server. We have two SQL Servers. Server B On server A, I created a linked server to server B

Now on Server A I have to do an insert on Server B DB. My chosen work is beautiful. Also I gave full access to user Below is the following error below.

OLE DB provider "SQLNCLI11" for linked server "serverB" returned the message "OLE DB multi-step actions generated errors. Check each OLE DB status value if available. Job failed."

Msg 7344 Level 16 State 1 Line 1 OLE DB provider "SQLNCLI11" for linked server "serverb" was unable to insert INSERT INTO into table "[serverb]. [Data]. [Dbo]. [Test]" due to column "test_ID". The user did not have write permission to the column