Is it permissible to perform a marriage contract with the intention mentioned in the question – for the purpose of making the relationship permissible and being able to communicate with the girl without feeling guilty – knowing that it is not possible to meet her currently, and will the doer of that be rewarded for his intention?

It is permissible to marry a righteous girl, and she should be given in marriage by a Muslim judge, or by an upright Muslim man with her consent if a judge is not available.

This can be done online, with the presence of the girl and two witnesses, in the presence of the mosque's imam. The marriage contract is conducted via video call, where the imam says: "I give you [name of girl] in marriage," and the suitor says: "I accept marriage to [name of girl]."

The unlawful relationship must be severed until the marriage contract is concluded.