How do we know that Norway has stopped fighting with Denmark?

In Act I Sc.2 Claudius the newly crowned king of Denmark announces that Prince Fortinbras of Norway, without the knowledge of his uncle the sick and bed ridden king of Norway is planning to attack Denmark and retrieve the territories which his father the previous king of Norway had ceded legally to Hamlet's father before his death. Claudius dispatches two of  his ambassadors Voltimand and Cornelius with letters to meet the present bedridden King of Norway and request him to check young Fortinbras and prevent him from marching to war with Denmark:

we have here writ
To Norway, uncle of young Fortinbras,--
Who, impotent and bed-rid, scarcely hears
Of this his nephew's purpose,--to suppress
His further gait herein; in that the levies,
The lists and full proportions, are all made
Out of his subject: and we here dispatch
You, good Cornelius, and you, Voltimand,
For bearers of this greeting to old Norway;
Giving to you no further personal power
To business with the king, more than the scope
Of these delated articles allow.

In Act IV Sc.4 we read of the same prince of Norway young Fortinbras seeking permission from the present king of Denmark Claudius to march through Denmark with his army to fight a battle with Poland. This is proof enough that Claudius's letters to the old King Norway in Act I Sc.2 have had their desired effect and young Fortinbras has been prevented from reclaiming the territories his father had legally ceded to Hamlet's father:

Go, captain, from me greet the Danish king;
Tell him that, by his licence, Fortinbras
Craves the conveyance of a promised march
Over his kingdom.

If young Fortinbras still harbored hostile territorial ambitions against Denmark, then he certainly would not have 'greeted' Claudius 'craving' for 'licence,' that is, permission to march through Denmark to launch a military operation against Poland.

Thus the conflict between the kingdoms of Denmark and Norway which is mentioned in Act I Sc.2 has certainly been resolved by Act IV Sc.4.