Put a TO for "old system" on the Relationships Graph for "new system". Create a relationship between them. Put the "old system" search field on a layout in the "new system".
To go there, write a script that uses Go to Related Record. Be sure to trap for the case when no record is present using IsEmpty ( old system::key field ).
And adding to Mike's advice, if the two are separate databases, set up the initial connection as an external data source (File > Manage > External Dat Sources…)
Which is done automatically when you put the TO on the Graph.
Well blow me down! That is why my motto is "always learning". I'd always set up the external data source first so hadn't discovered that trick. Thanks Mike.