A short put is equivalent to a covered call position at the same strike (i.e. long stock and short call with the same strike price as the put).
A covered call can be ITM too. You can create the same ITM short put by selecting the appropriate strike to set up a covered call.
It doesn't matter whether it is ITM, ATM or OTM. Synthetics always use the same strike(s). For example, say the stock is at 50. If you have a short 60 put then it is ITM. A synthetic position would be long stock + short 60 call. In other words, an ITM short put is equivalent to an OTM covered call.
Simplified example of MTE's explanation: Long 100 shares XYZ @ 50 Short 1 Jul 60 call @ 1 vs Short 1 Jul 60 put @ 11 Run the expiration values for any price. P&L is identical.