Yes! an A1 rated Organisation may issue an EASA an EASA Form 1 for any component removed serviceable from an EU registered aircraft, as long as certain conditions are fulfilled. Let is see how…

Within the EASA regulatory framework, an Organization (Company) can be approved under one or more different “Classes” and different “Ratings”
There are 4 different classes with their related ratings (in brackets):

• Aircraft (A1, A2, A3, A4),
• Engines (B1, B2, B3),
• Components (C1, C2, C3….C22),
• Specialized Services (D1)

It is not the intention of this article to provide with a detailed explanation of the ratings and the related privileges for the organizations that hold them, what it is worth to mention here is that A1 Organizations are authorized to carry out maintenance on Aircraft like Boeing B777 or Airbus A380 (just to make an example), while B1 Organizations are authorized to carry out maintenance on engines (like GE-90 or Rolls-Royce Trent 100 (again just for example).

Similarly, C rated organizations are authorized to carry out maintenance on components, other than engines (for example, a C14 rated organizations can maintain Landing gears).
For the sake of completeness, a D1 rated Organization refers to NDT services (Non Destructive Test, like X-Ray).

A1 rated organizations release their maintenance works in a document called Certificate of Release to Service (CRS), which is a document (a certificate) with a layout arranged by the company according to guidelines provided by the EASA.
B, C and D rated organizations release their work in a document called EASA Form 1, which is still a CRS but with a layout predefined by the EASA.

However the peculiarity of the EASA Form 1 is that it may also be used to “declare something”, as below explained.

An A1 rated organization is not supposed to issue CRS for works on engines or components, if such organization is not also approved under engine and component class ratings (so for example a Company who holds A1 along with B1 and C14).

This can be done in accordance with the regulation EASA Part 145 in its AMC2 145.A.50(d) (at least until today in March 2018).
To figure out the usefulness of such possibility, you can think to a Line Maintenance Organization (A1) who would like to swap engines from different aircraft, so that the serviceable engine can be installed where it is required to be installed for the sake of the operations.

The conditions are quite hard to be all met, anyway they are the following:

• The Organization should ensure that the component was removed from aircraft by an appropriately qualified person.
• The aircraft component may only be deemed serviceable if the last flight operation with the component fitted revealed no faults on that component/related system.
• The aircraft component should be inspected for satisfactory condition including in particular damage, corrosion or leakage and compliance with any additional maintenance data.
• The aircraft record should be researched for any unusual events that could affect the serviceability of the aircraft component such as involvement in accidents, incidents, heavy landings or lightning strikes. (Under no circumstances may an EASA Form 1 be issued if it is suspected that the aircraft component has been subjected to extremes of stress, temperatures or immersion which could affect its operation).
• A maintenance history record should be available for all used serialized aircraft components.
• Compliance with known modifications and repairs should be established.
• The flight hours/cycles/landings as applicable of any service life-limited parts including time since overhaul should be established.
• Compliance with known applicable airworthiness directives should be established.
• The issued EASA Form 1 (showing INSPECTED/TESTED in its block 11) should identify the aircraft from which the component was removed and should also specify information described in the mentioned AMC2 145.A.50(d) (in the point 2.4).

It is worth to say that you have always to agree beforehand with your assigned EASA inspector before applying what above written.

Eventually, should be noted that what above written refers to an A1 rated organization because it seems to the writer the best application of the rule but it should be then remarked that the regulation (in the AMC2 145.A.50(d))  mentions that “serviceable aircraft components removed from an EU Member State registered aircraft may be issued with an EASA Form 1 by an appropriately rated organization” subject to the conditions above listed.
(Unfortunately definition of “appropriated rated organization” is not given in the regulation).