General :: How To Transfer Data From One Database To Another

I recently designed a new database according an old database in order to replace it. I found that I have trouble transferring the data from old to new database.

Only transferring data from one table to another

Database A: [table]![customer]
to
Database B: [table]![Client]

Field name on both are different

DatabaseA:
Table Customer:
Name,
PhoneNumber,
e-mail.

DatabaseB:
Table Client:
FullName,
HomePhone,
CellPhone,
E-mail.

How can I transfer from "Database A/table customer" to "Database B/table Client"?