DoD Tier 5 investigation to DHS Tier 2 reciprocity

I currently have a current and favorably awarded DoD Tier 5 security clearance (TS SCI). I have recently accepted a position with DHS that requires a Tier 2 Public Trust Investigation (Mod. Risk Non-IT). Will my current DoD clearance be reciprocated to the DHS considering it’s going from a clearance to a public trust position? Also, if you have been in a similar situation, what is the reciprocity timeline?

Thanks in advance!