I want How to archive transaction data older than 3 months and move those data to Archival DB via SP ?

To get the last three month transaction you try like this below query :
Declare @ThreeMonth_Before datetime=DateAdd(mm,-3,getdate())

select *
from YOURTABLE_NAME
where
YOUTRANSACTION_DATE >=@ThreeMonth_Before

here i get three month below date from current date and check in table where the transactiondate is greater then before 3 month.this will result 3 month all data from your table.

Now create a insert query with this select and inrest the result to your tables .
Make a SP and paste your query and execute it.

Are you referring to transaction logs? If so, have you tried log shipping? Please let me know.