[Solved] Copy data from a table of a database to a table of another database in SQL Server

1) First you Export the data into the other Server :

Right Click on Database->Tasks->Exports Data->Select DataSource(Current Server)->Select Destination(Choose new server)->Select Objects to be copied->Finish.

Now Once the Export task will done then use Update query to your destination database and delete the exported table..

IF(EXISTS(Select * from [DatabaseName.dbo.DestinationTableName]))
BEGIN
	Update Databasename.dbo.[TableName in Server 2]
	Set columnName = databaseName.dbo.Tablename.ColumnName From ExportedTableName
END
ELSE
BEGIN
	INSERT INTO DatabaseName.dbo.[TableName in server 2] (ColumnName)
	Select ColumnName From dbo.databaseName.TableName 
END 
Delete FROM DatabaseName.dbo.ExportedTableName

This might Help!!