If you can't come up with more information from the manufacturer, then what Dave has suggested may be your only option. Here are my concerns:

1. What is the frequency of the modulated IR carrier? I found two datasheets from Philips [Link: semiconductors.philips.com] and [Link: semiconductors.philips.com]

Philips, IIUC, created the RECS80 protocol. Those data sheets (for RECS80 transmitters) show three different IR protocol variations for a RCECS80 transmission. Flasher Mode(unmodulated) and two Modulated modes one with an additional bit and a different start sequence. Both modulated modes use a ~38 KHz modulation frequency, but the tranmitter chips do use a 455KHz clock for timing (but the modulation frequency is 1/12 of the clock).

2. How many bits does the Gira protocol use? The RECS80 Flasher mode and one modulated mode use a toggle bit followed by three sub-device bits and six command bits. Since the start sequence looks like a bit, I could say that is 11 bits. However the other modulated mode has a Toggle bit, four sub-device bits and six command bits, but its start sequence is two short bits. To me that would be 13 bits.

So to generate the command, then we would need to know the IR modulation frequency AND to resolve the "12 bit PCM" question. We would also need to have some idea what the sub-device and command values are or you will need to test a lot of commands, again suggesting Dave's method.

It isn't unheard of for an IR command to be the same protocol at a much higher frequency. Kenwood has used the NEC1 protocol at 455 KHz. But, I do think the Pronto should be able to learn the 38KHz or the 0KHz flasher mode that would suggest the higher frequency (unless the batteries are bad in the OEM remote and should always be replaced when encountering learning problems).