Transportation of goods

Yes, Recipient can very well take/claim input tax credit of IGST, it doesn't matter that both have same state GSTIN or not.

Whether a transaction is Inter-State supply or Intra-State Supply, it should be determined based on location of the supplier and the place of supply. 

With effect from 01.02.2019 for transportation of goods to a place outside India, the place of supply shall be the place of destination of such goods i.e outside india. So, this transaction considered as inter state transaction an accordingly IGST charged.

But place of supply is other territory, so isn't it is ineligible input,

or please provide notification number and it's date

According to Section 2 (62) “input tax” in relation to a registered person means tax ( any tax i.e. CGST, SGST, UGST or IGST ) charged on any supply of goods or services or both made to him ( registered person )

ITC of Input tax charged on any supply of goods or services or both and such Supply are used or intended to be used in the course or furtherance of his business is available as per Section. 16(1) of GST Act. subject to conditions prescribed u/s 16(2) to 16(4) read with rule 36 like tax invoice have a GSTIN of recipient ect. except it's Block Input Tax Credit as per section 17 (5) of GST Act or your output Supplies is exempt supply under GST.

So, in your case it's not blocked u/s 17(5) nor you are supplying exempt Goods/service (assumed) than you can take Input tax credit subject to fulfillment of condition prescribed u/s 16 of Act.

Place of Supply is used to determine whether goods is inter state or intra state and to charge GST accordingly, it doesn't affect the availability of Input tax credit to taxpayer.