Hi D.
1. Thanks for yor answer but I'm not sure if my problem is now solved 
2. PDATE... Where do I define it? In T77S0 is no entry and in the profile too
3. The user IS authorized in that time period. Only thing by this profile is, that we modified the end date of the time slice +1 day because some policies (IT0000) are applied to the employee 1 day after he switched the organizational assignment. So we got the fact that the user has 1 Profile for time 01.01. - 30.09 and 1 profile with time 01.01. - 01.10.
That's important for some reports which are accomplished 1 year later or so...
The History Profile is the last one so the write access should be given for example at the 01.02, right?
4. The switch for the custom Infotype is activated in V_T582A
5. Point 3 in the F1 Help is correct I think but I thought if the user has read or write access I can overwrite with my profile?
BTW: Infotypes with time period 3 are working fine...