Is it a single-table record? Are there attachments?
If the answer is that it's a single-table record and there are no attachments you can use a Table-to-Table import which you would need to fire using a button to launch it from the record you are pushing. The button would usually have to "mark" the record in some way (like a checkbox) and then run the Table-to-Table Import in the other Application which can then come back to the record and mark it as "transferred" with a date/time field. There are also other more advanced options for marking a record which doesn't do all this; but ultimately when transferring data, unless you are then deleting it from the source table; it's a good idea to mark it as transferred.
You have to do this so that the next record that is pulled in the table-to-table import doesn't import the same record again that were already transferred.
If you do have attachments, then you may want to consider pulling the data via the Table-to-Table import and populating a cross-app-Relationship so that you can access the file attachments in Application B when the attachments exist in Application A.
Users would need access to both apps to do all of this because it would be their User permissions creating records in Application B from Application A.