diff --git a/packages/@aws-cdk/aws-scheduler-targets-alpha/lib/lambda-invoke.ts b/packages/@aws-cdk/aws-scheduler-targets-alpha/lib/lambda-invoke.ts
index 69c26048c701f..bbd986780b6bd 100644
--- a/packages/@aws-cdk/aws-scheduler-targets-alpha/lib/lambda-invoke.ts
+++ b/packages/@aws-cdk/aws-scheduler-targets-alpha/lib/lambda-invoke.ts
@@ -1,34 +1,23 @@
 import { ISchedule, IScheduleTarget } from '@aws-cdk/aws-scheduler-alpha';
-import { Names } from 'aws-cdk-lib';
 import { IRole } from 'aws-cdk-lib/aws-iam';
 import * as lambda from 'aws-cdk-lib/aws-lambda';
 import { ScheduleTargetBase, ScheduleTargetBaseProps } from './target';
-import { sameEnvDimension } from './util';
 
 /**
  * Use an AWS Lambda function as a target for AWS EventBridge Scheduler.
  */
 export class LambdaInvoke extends ScheduleTargetBase implements IScheduleTarget {
+  private readonly func: lambda.IFunction;
+
   constructor(
-    private readonly func: lambda.IFunction,
-    private readonly props: ScheduleTargetBaseProps,
+    func: lambda.IFunction,
+    props: ScheduleTargetBaseProps,
   ) {
     super(props, func.functionArn);
+    this.func = func;
   }
 
-  protected addTargetActionToRole(schedule: ISchedule, role: IRole): void {
-    if (!sameEnvDimension(this.func.env.region, schedule.env.region)) {
-      throw new Error(`Cannot assign function in region ${this.func.env.region} to the schedule ${Names.nodeUniqueId(schedule.node)} in region ${schedule.env.region}. Both the schedule and the function must be in the same region.`);
-    }
-
-    if (!sameEnvDimension(this.func.env.account, schedule.env.account)) {
-      throw new Error(`Cannot assign function in account ${this.func.env.account} to the schedule ${Names.nodeUniqueId(schedule.node)} in account ${schedule.env.region}. Both the schedule and the function must be in the same account.`);
-    }
-
-    if (this.props.role && !sameEnvDimension(this.props.role.env.account, this.func.env.account)) {
-      throw new Error(`Cannot grant permission to execution role in account ${this.props.role.env.account} to invoke target ${Names.nodeUniqueId(this.func.node)} in account ${this.func.env.account}. Both the target and the execution role must be in the same account.`);
-    }
-
+  protected addTargetActionToRole(_schedule: ISchedule, role: IRole): void {
     this.func.grantInvoke(role);
   }
 }
\ No newline at end of file
diff --git a/packages/@aws-cdk/aws-scheduler-targets-alpha/test/lambda-invoke.test.ts b/packages/@aws-cdk/aws-scheduler-targets-alpha/test/lambda-invoke.test.ts
index 8439776023afd..2fcb2a8d30629 100644
--- a/packages/@aws-cdk/aws-scheduler-targets-alpha/test/lambda-invoke.test.ts
+++ b/packages/@aws-cdk/aws-scheduler-targets-alpha/test/lambda-invoke.test.ts
@@ -319,42 +319,38 @@ describe('schedule target', () => {
     });
   });
 
-  test('throws when lambda function is imported from different account', () => {
-    const importedFunc = lambda.Function.fromFunctionArn(stack, 'ImportedFunction', 'arn:aws:lambda:us-east-1:234567890123:function/somefunc');
-
-    const lambdaTarget = new LambdaInvoke(importedFunc, {});
-
-    expect(() =>
-      new Schedule(stack, 'MyScheduleDummy', {
-        schedule: expr,
-        target: lambdaTarget,
-      })).toThrow(/Both the schedule and the function must be in the same account/);
-  });
-
-  test('throws when lambda function is imported from different region', () => {
-    const importedFunc = lambda.Function.fromFunctionArn(stack, 'ImportedFunction', 'arn:aws:lambda:us-west-2:123456789012:function/somefunc');
+  test('using imported lambda function should not throw', () => {
+    const lambdaFuncArn = 'arn:aws:lambda:us-east-1:234567890123:function/somefunc';
+    const importedFunc = lambda.Function.fromFunctionAttributes(
+      stack,
+      'ImportedLambdaFunction',
+      {
+        functionArn: lambdaFuncArn,
+        skipPermissions: true,
+      },
+    );
 
     const lambdaTarget = new LambdaInvoke(importedFunc, {});
-
-    expect(() =>
-      new Schedule(stack, 'MyScheduleDummy', {
-        schedule: expr,
-        target: lambdaTarget,
-      })).toThrow(/Both the schedule and the function must be in the same region/);
-  });
-
-  test('throws when IAM role is imported from different account', () => {
-    const importedRole = Role.fromRoleArn(stack, 'ImportedRole', 'arn:aws:iam::234567890123:role/someRole');
-
-    const lambdaTarget = new LambdaInvoke(func, {
-      role: importedRole,
+    new Schedule(stack, 'MyScheduleDummy', {
+      schedule: expr,
+      target: lambdaTarget,
     });
 
-    expect(() =>
-      new Schedule(stack, 'MyScheduleDummy', {
-        schedule: expr,
-        target: lambdaTarget,
-      })).toThrow(/Both the target and the execution role must be in the same account/);
+    Template.fromStack(stack).hasResourceProperties('AWS::IAM::Policy', {
+      PolicyDocument: {
+        Statement: [
+          {
+            Action: 'lambda:InvokeFunction',
+            Effect: 'Allow',
+            Resource: [
+              lambdaFuncArn,
+              `${lambdaFuncArn}:*`,
+            ],
+          },
+        ],
+      },
+      Roles: [{ Ref: 'SchedulerRoleForTargetfdfcef0FF637F7' }],
+    });
   });
 
   test('adds permissions to DLQ', () => {