Trigger Between Two Tables In Separate Db

I am new to T-SQL and triggers
Any help will be appreciated

I am trying to change this code to insert firstname, surname (taken from employee table on db A) to firstname, surname on customer table of DB B but also create cust_id on customer table and DB B. currently I am getting all rows of customer.cust_id filled with the same data whenever a new data is inserted into (firstname,surmname of employee table)

Create trigger gen_cust_id ON employee for insert
AS
Update customer SET cust_id =( SELECT
Replicate('0',(4-DATALENGTH(CONVERT(varchar(10),i.id))))
+ Convert (varchar(10),i.id)
+ Substring(i.lastname,1,3)
+ Substring(i.firstname,1,1)
from employee C INNER JOIN inserted i on i.id=c.id)
from employee C INNER JOIN inserted i on i.id=c.id

Saad