May an Estonian enter Germany at FRA during COVID-19?

According to an e-mail from the border section of the German federal police headquarters, the restrictions only apply when arriving from Austria, Denmark, France, Italy, Luxembourg, Spain, Switzerland or from outside Schengen.

However, the TIMATIC database, used by airlines, states the restrictions apply everywhere. Since IATA gets their info from the federal police headquarters (at least in part), this confuses me and I am in fact seeking clarification on this as we speak.

TIMATIC states:

Passengers are not allowed to enter Germany.

[...]

This does not apply to passengers with evidence that their travel is to perform a professional activity, e.g., commuters, diplomats, nursing staff, food industry personnel, specialists

So in practice, the check-in staff in Tallinn will require evidence of your business activity.

Summary: For entering Germany, work is a valid reason - they shoud bring documentation that they will be working.

Once inside Germany, they may be required to quarantine for 14 days. This is expected to be relaxed for inner-EU travel any day now.

The Corona virus FAQ of the federal ministry of internal affairs (BMI) says:

What are urgent reasons for crossing the border?
 [...]

The cross-border flow of goods and cross-border travel for work purposes are permitted (including for commuters, members of the European Parliament and accredited diplomats), irrespective of the traveller’s nationality. Cross-border travel to carry out professional contractual services is also permitted. Commuters must carry appropriate documentation (e.g. work contract, project contract/documents, permit for frontier workers) as proof of the need to cross the border for work.

and

What restrictions are in place on air travel within the European Union?

On 18 March 2020, Federal Minister Seehofer, in coordination with the EU Member States affected, extended temporary border control to include air traffic within the European Union, in order to further contain the spread of the coronavirus. Checks at Germany’s borders were imposed immediately and include flights from Italy, Spain, Austria, France, Luxembourg, Denmark and Switzerland.

For travellers who have no urgent reason to travel, immediate restrictions apply to these travel routes. Travellers who have an urgent reason to travel, and cross-border commuters, are required to provide appropriate proof of the necessity to cross the border.

The Federal Ministry of the Interior urges citizens not to travel unless it is absolutely essential.

Since Frankfurt is in Hesse, the Hessian Corona-Verordnung applies once they are inside Germany.

It prescribes that in general anyone entering Hesse from abroad has to directly go into quarantine for 14 days and contact the local health authorities about this.

However, there are exemptions for people entering in oder to work (exemptions in the sense that instead of them quarantining theemselves, their employer or business partner can take safety precautions and register the case with the health authorities). Please check the actual text for details.

Also, if they are only transiting Hesse (you are in another Land), also check the regularions there.

The BMI press release of May 13th discusses recent relaxation of border controls and also says:

 The federal states are encouraged to revise their quarantine regulations for arriving and returning travellers as needed. A 14-day quarantine should be ordered in future only for travellers entering Germany from countries outside of the EU.