You can issue invoice charging IGST. In GST registration is origin based and NOT destination based or consumption based. This is very much clear from Section 22 (1) of CGST Act In terms of Section 22 (1) of CGST Act, the supplier is required to be registered in State or U.T. FROM WHERE that person makes a taxable supply of goods or services or both. See the definition of "place of business" under Section 2 (85) of CGST Act which is as follows :
(85) “place of business” includes -
(a) a place from where the business is ordinarily carried on, and includes a warehouse, a godown or any other place where a taxable person stores his goods, supplies or receives goods or services or both; or
(b) a place where a taxable person maintains his books of account; or
(c) a place where a taxable person is engaged in business through an agent, by whatever name called.
What I want to say , 'Place of business' is determining factor for registration.
For legal backing go through this decision AAR Karnataka :
2020 (36) G.S.T.L. 239 (A.A.R. - GST - Kar.) = 2020 (4) TMI 693 - AUTHORITY FOR ADVANCE RULING, KARNATAKA IN RE : T & D ELECTRICALS