Yes,everybody is entiteld to make a claim to the "Finanzamt".No matter who or what he/she represents.The question is if you get something from them.
In the first instance I would get the necessary form for an "Einkommenssteuerrueckerstattung" and fill it in.The form is available under the web page of the " Finanzamt".
If your relatives are moving for job reasons than the "Arbeitsamt"will even pay their moving costs,provided they have a new permanent job here.
There are several companies engaged in tax matters for that particular case,try the web under "Steuerberater + Umzug ".These companys work of course for a fee,some charge fix costs,other a percentage (no win-no fee).
Make sure your relative gets his "Lohnsteuerkarte" from his employer.He needs at least his personal number which is shown on it.
Income taxes (for the PAYE workers in Germany) are in general deducted straight away from the wage at source.
The best thing would be for him to contact the necessary authoritys as long as they are still in Germany.